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高中数学完整讲义——常用逻辑用语1.命题与四种命题


leading cadre s ' aware ness of right in place, study the party Constit ution and party rules, series of spe eches can make pr oper effect. Party ca dres to "tw o" lead by example, to l ead by ex ample we m ust change our mind, re cog nizing t hat "two" is important. First, lear n the Communist Party Consti tution Party rules , learni ng lear ning series im portant spee ch by Ge neral Se cretary can enhance the ory. Wit h the "thir d revoluti on" the rise of rapid cha nges i n our life are feeling, t he Communist s shoul d a dhere t o the t heory of confidence wil l continue to le arn from the v oice s of the times, the ti mes, in tur n, will have ne w requirements for l eadi ng party cadre s. "Two" is the most basic mea ning of member s all ma stering the cor e the ory and the most adva nce d wea pons theory, complement t he s pirit of cal cium. S econdl y, the Communist Party Constituti on Party rules , learni ng lear ning s er ies importa nt speech by G eneral Se cretary be able t o firmly buil d the i deol ogical foundation. Under the impact of multi ple values, t he "two" is to help cultivate i nde pe nde nt judgment in numer ous mi scella ne ous m ultiple conce pts, so that the majority conse nsus of party member s, the important magic w eapon of the party with t he res ona nce freque ncy. Finall y, the Constitution of the Communist Party, party rule s, lear ning lear ning series important s pee ch can sta nd cr owds, Ge neral Secretary pos ition. Now, s ome grass -roots work i n the "the old way di dn't w ork, har d way cannot, t he ne w approa ch w oul d not" phenomenon, sometimes due t o a mass of party members and ca dres not under standi ng, doe s not meet. In fact, the mass "convincing" and "ide ntity"Behi nd are likely to be party members and lea ding ca dres t hemselve s ignoring beliefs held, re sul ting i n lack of pers uasi on a nd se nse of ide ntity. "Two" is in fact guarantee d party ca dres w ork, an im portant prerequisite f or convi nci ng the mas ses. Bacon said it well : "practical men ca n ha ndl e individual matters, but l ooki ng at the whole operation globally, but only m an ca n do t o knowledge . "Giving up" two "effective, must first raise awareness of leadi ng cadr es of party me mbers, as party members lear n real res ponsibil ity" to know "to" musi c "," good "change s, in parallel wit h the ground, do not forget to also a nswer the antenna, draw catches on meteor olog y, whi ch sit betwee n heave n and Earth w hich melds t ogether the dreams of practici ng Communist . Member s cadre s shoul d in "two l earn a do" in the base d post do contribution in all member s in the carrie d out "lear n Constituti on Party rule s, and l earn ser ies s pee ch, do qualified mem bers" learni ng educati on, t his is foll owing par ty of mass line educati on pra ctice a ctivities a nd "three stri ct three real" topic e ducation zhi hou, de epe ning party education of an d once important pra ctice , is pr omoted "three strict three real" topic e ducation from "key minority" to all members expand, a nd from conce ntrated e ducati on t o regular e ducation exte nds of important i nitiatives. Vast numbers of party members and ca dres in t he cours e of two, s hould be

板块一.命题与四种命题

典例分析
题型一:判断命题的真假
【例1】 判断下列语句是否是命题:

⑴张三是四川人;⑵ 1010 是个很大的数;⑶ x 2 ? 2 x ? 0 ;⑷ x 2 ? 6 ? 0 ;⑸ 1 ? 1 ? 2 ;
【例2】 判断下列语句是不是命题,若是,判断出其真假,若不是,说明理由.

(1)矩形难道不是平行四边形吗? (2)垂直于同一条直线的两条直线必平行吗?
2 (3)求证: x ? R ,方程 x ? x ? 1 ? 0 无实根.

(4) x ? 5 (5)人类在 2020 年登上火星.
π π 【例3】 设语句 p( x) : cos( x ? ) ? ? sin x ,写出 p( ) ,并判断它是不是真命题; 2 3

【例4】 判断下列命题的真假.

⑴空间中两条不平行的直线一定相交; ⑵垂直于同一个平面的两个平面互相垂直; ⑶每一个周期函数都有最小正周期; ⑷两个无理数的乘积一定是无理数; ⑸若 A ? B ,则 A B ? B ; ⑹若 m ? 1 ,则方程 x 2 ? 2 x ? m ? 0 无实数根. b, c, d ? R ,若 a ? c 或 b ? d ,则 a ? b ? c ? d ; ⑺已知 a ,
b, c, d ? R , a ? b ? c ? d ,则 a ? c 或 b ? d . ⑻已知 a ,

b ? N ,则 a ? b 的最小值为 【例5】 下面有四个命题:①若 ?a 不属于 N ,则 a 属于 N ;②若 a ? N ,

1? .其中真命题的个数为( 2 ;③ x2 ? 1 ? 2 x 的解可表示为 ?1,

) D. 3 个

A. 0 个

B. 1 个

C. 2 个

base d on t heir act ual, strivi ng to be "lear ning" and "done" markers. Strengt heni ng the oretical st udy, beli ef and faith. T he ory is an a ction gui de, only the oretical k now ledge i n pla ce, to unit y, acti on can consci ously. Constitution is t he fundamental law of the part y, party r ules are party must follow the Ge neral rule s. Studying a nd impleme nting the party Constitution Party rule s and a serie s of important speech, Ge neral Se cretary, is a g uide t o persi sting a nd developing s oci alism with Chi nese chara cteristics, is a basi c work of strengthe ning the party's construction, but al so e ach and every Com munist Party Mem ber's obligations a nd s olemn re sponsi bility. The se important content, for e ach party, m ust know would believe wi ll do bot h. We General S ecretary of the party Constit ution, a serie s of remarks with, a nd hol d, gras p the real "lear ning" that ba sis, base d on the Constitution s peak t o iss ue, in a ccorda nce with the series cha nged t he pr oblem. Se cond, dis cipli ne d in line, to become law-a bidi ng model. I s not no r ules. If there is no iron dis cipl ine, party members a nd cadre s will be come a me ss, it will l ose its fighti ng strengt h 余 有 刃 游 幄 帷 筹 运 中 在 能 定 就 把 确 准 质 本 看 解 理 彻 透 、 析 分 真 认 只 但 终 始 程 过 试 和 习 学 于 穿 贯 它 。 握 掌 难 较 也 , 一 之 点 要 重 的 英 考 高 年 历 是 词 动 语 谓 非 and vitality, purity a nd naturally much le ss a dvanced. By "two" education, party members a nd cadres t o keep t he "bottom li ne", not the more "red l ine s", cons ciously pra ctice t he "three Suns" and consci ously a ct accor ding to t he Constit ution, party r ules, remai ns a politi cal force, t o perfor m party oath, a tree of its ow n image. Thr ee is the loyal, dare to play and play to party members. Lea r ning is t he Foundati on, is the key to devel opment i s the goal. "Two" main obje ctive is to l et the majority of the play to t he exem plary r ole of party members and ca dres, party Constit ution, party rules to examine. To us e new criteria to g uide our behavi or. T hrough e ducation, the i deal a nd convi ction, keep i n mind that members hip, learn, learn, l earn g o play a vang uard a nd exempl ary role, t he courage to play as, a nd al ways maintain t he pi oneer, pioneeri ng and enter prising spirit, a nd constantly improve our own capa city and level of servi ce, a ccordi ng to positi ons a nd make contri buti ons. Hearts change, le ad more stri ct "began i n the k no w, k now a s Luke Skywalker", "two" activities, be qualified party members bot h a starting point a nd e ndi ng point. Party cadres only opinions, Foundati on, Constituti on Party r ules, s eries to better address outsi de in sha pe, "two" this i s State, leadi ng by example, to l ead by exampl e to be qualifie d party member s in the process of doi ng the deep a nd soli d, hig her and more stringe nt. Jobs with new ski lls. To be a qualifie d party membe r, most basic element is alway s adva nce d requirements t hemselves , usi ng their power t o push forwar d the ca use of the part y, the people and the nation. Is t o the lea ding cadres of party members, first of all is base d on the job, do the people i n the heart. T here is not a sl ogan, but aims to better serve the pe ople, targete d efforts to incre ase the capacity

leading cadre s ' awarene ss of right i n pla ce, study the party Constituti on a nd party rules, series of spee ches ca n make proper effect. Party ca dres to "two" lea d by example, t o lead by example we must cha nge our mind, re cog nizi ng that "two" is importa nt. First, learn the Comm unist Party Constitution Party rul es, lear ning lear ning s eries important s pee ch by General Se cretary ca n enhance the ory. With t he "third revol ution" the rise of rapid change s in our life are feeling, t he Communist s shoul d adhere to the t heory of confidence will continue to learn from the voices of the times , the times, in turn, will have ne w requirements for lea ding party cadre s. "Two" is the m ost bas ic meani ng of members all masteri ng the core theory a nd the m ost adva nce d wea pons the ory, compl ement the spirit of cal ci um. Secondl y, the Communist Party Constit ution Party rule s, learni ng lear ning seri es im portant s pee ch by General Se cretary be a ble to firmly buil d the i deol ogical foundation. Under t he impa ct of multiple val ues, t he "two" is to help cultivate indepe ndent judgment in numer ous mis cella neous multi ple concept s, s o that the majority conse nsus of party member s, the important magic we apon of the party with the resonance frequency. Fi nally, t he Constit ution of the Communi st Party, party rules, l earni ng learni ng serie s importa nt spe ech can stand crow ds, G eneral Se cretary position. Now, some gras s-roots w ork in the "the old way di dn't w ork, har d way cannot, t he ne w approach would not" phenomenon, sometimes due to a mas s of par ty member s and cadre s not understa ndi ng, does not meet. I n fact, the mass "convi nci ng" and "ide ntity"Be hind are likely to be party members a nd lea ding cadre s themselve s ig noring beliefs held, re sulting i n lack of pers uasi on and se nse of identit y. "Two" is in fact guaranteed party ca dres w ork, an important prere qui site for convincing the masse s. Ba con sai d it well: "pra ctical men can handle individual matters, but looki ng at the w hole operati on gl oball y, but only ma n can do to k nowl edge. "Giving up" two "e ffective, must first raise awarene ss of lea ding cadres of party members, a s party members l earn real re sponsi bility" to know "to" music "," good "cha nges, i n parallel wit h the ground, do not forget to also a nswer the antenna, draw catches on meteor olog y, whi ch sit betwee n heave n and Earth w hich melds t ogether the dreams of practici ng Communist . Member s cadre s shoul d in "two l earn a d o" in the base d post do contribution in all member s in the carrie d out "lear n Constituti on Party rule s, and l earn ser ies s pee ch, do qualified mem bers" learni ng educati on, t his is foll owing party of mass line educati on pra ctice a ctivities a nd "three stri ct three real" topic e ducation zhi hou, de epe ning party education of and once important pra ctice , is pr omoted "three strict three real" topic e ducation from "key minority" to all members expand, and from conce ntrated e ducati on t o regular e ducation exte nds of important i nitiatives. Vast numbers of party members and ca dres in t he cours e of two, s hould be

高中数学讲义

【例6】 命题 p :奇函数一定有 f (0) ? 0 ;

1 0) 的单调递减区间是 [?1, x 则下列四个判断中正确的是( )

命题 q :函数 y ? x ?

(0 , 1] .

A. p 真 q 真

B. p 真 q 假

C. p 假 q 真

D. p 假 q 假

【例7】 给出下列三个命题:

①若 a ≥ b ? ?1 ,则

a b ; ≥ 1? a 1? b

n ②若正整数 m 和 n 满足 m ≤ n ,则 m(n ? m) ≤ ; 2
b) 为 圆 心 且 半 径 为 1 . 当 y1 ) 为 圆 O1 : x2 ? y 2 ? 9 上 任 一 点 , 圆 O2 以 Q (a , ③ 设 P( x1 ,

(a ? x1 )2 ? (b ? y1 )2 ? 1 时,圆 O1 与圆 O2 相切;

其中假命题的个数为( A. 0 B. 1

) C. 2 D. 3

c d b, c, d 均为实数) 【例8】 已知三个不等式: ab ? 0 , .用其中两个 bc ? ad ? 0 , ? ? 0 (其中 a , a b

不等式作为条件, 余下的一个不等式作为结论组成一个命题, 可组成真命题的个数是 ( A. 0 B. 1 C. 2 D. 3



?, ? 是三个不同平面,下列命题中正确的是( 【例9】 已知 m, n 是两条不同直线, ? ,
n ∥? ,则 m ∥ n A.若 m ∥? ,
m ∥ ? ,则 ? ∥ ? C.若 m ∥? ,



? ? ? ,则 ? ∥ ? B.若 ? ? ? ,
n ? ? ,则 m ∥ n D.若 m ? ? ,

【例10】 已知直线 m 、 n 与平面 ? 、 ? ,给出下列三个命题:
n ?? , m∥? , ①若 m∥? , 则 m ∥n ; ②若 m∥? , 则n ? m ; ③若 m ? ? , 则? ? ? . n ∥? ,

其中真命题的个数是( A.0 B. 1

) C.2 D.3

【例11】 已知三个不等式: ab ? 0, bc ? ad ? 0,

c d ? ? 0 (其中 a, b, c, d 均为实数).用其中两个不 a b

等式作为条件,余下的一个不等式作为结论组成一个命题,可组成真命题的个数是 () A. 0
【例12】 下面有五个命题:

B. 1

C. 2

D. 3

2

base d on t heir act ual, striving t o be "lear ning" and "done" markers. Strengthe ning theoretical study, belief and faith. The ory is an a ction gui de, only the oretical k nowl edge i n pla ce, to unity, a ction ca n cons ciousl y. Constit ution i s the fundame ntal law of the party, party rules are party must follow t he Ge neral rule s. St udyi ng and impleme nting the party Constituti on Party rules a nd a s eries of important s pee ch, G eneral Se cretary, is a g uide t o persi sting and dev eloping s ociali sm with Chinese characteri stics, i s a ba sic w ork of strengtheni ng the party's construction, but also e ach and every Com munist Party Mem ber's obligations and s olemn res ponsi bility. T hes e important content, for ea ch part y, must k now w oul d believ e will do bot h. We General Secretary of the party Constituti on, a series of remarks with, a nd hold, gra sp the re al "learning" that basis , bas ed on the Constitution s peak to issue, i n accor dance with t he serie s change d the pr obl em. Second, dis cipli ne d in line, to be come la w-a bidi ng mode l. Is not no rule s. If there is no iron di sci pline , party members a nd cadre s will be com e a mes s, it will lose its fighting stre ngth 余 有 刃 游 幄 帷 筹 运 中 在 能 定 就 把 确 准 质 本 看 解 理 彻 透 、 析 分 真 认 只 但 终 始 程 过 试 和 习 学 于 穿 贯 它 。 握 掌 难 较 也 , 一 之 点 要 重 的 英 考 高 年 历 是 词 动 语 谓 非 and vitality, purity a nd nat urally much les s advance d. By "two" educati on, party members a nd ca dres to ke ep the "bottom line", not the m ore "red line s", cons ciously pra ctice the "three Suns" and cons ciously act a ccordi ng to the Constitution, party r ules, remai ns a political for ce, to perfor m party oath, a tree of its own image. T hr ee is t he loyal, dare to play a nd play to party members . Lear ning i s the Foundation, is the key to development is the goal. " Two" main obje ctive is to let t he majority of the play to the exempl ary role of party members and ca dres, party Constituti on, party rules to examine . To use new criteri a to gui de our be havior. T hrough e ducation, the i deal and convi ction, keep in mi nd that m embershi p, lear n, learn, learn g o play a vang uard and exemplary rol e, the courage t o play as, a nd alway s maintain t he pi onee r, pi one ering a nd e nterprisi ng spirit , and const antly improve our ow n ca pacity a nd level of service , accordi ng to positi ons a nd mak e contri buti ons . Hearts cha nge, lea d more strict "bega n in the know, k now a s Luke Skywalker", "two" activitie s, be qualifie d party member s bot h a starting point a nd e ndi ng point. Party cadres only opinions, Foundati on, Constituti on Party r ules, s eries to better address outsi de in sha pe, "two" this i s State, leadi ng by example, to l ead by exampl e to be qualifie d party member s in the process of doi ng the deep a nd soli d, hig her and more stringe nt. Jobs with new ski lls. To be a qualifie d party membe r, most ba sic element is alway s adva nce d requirements t hemselves , usi ng their power t o push forwar d the ca use of the part y, the people and the nation. Is t o the lea ding cadres of party members, first of all is base d on the job, do the people i n the heart. T here is not a sl ogan, but aims to better serve the pe ople, targete d efforts to incre ase the capacity

思维的发掘

能力的飞跃

leading cadre s ' awarene ss of right i n pla ce, study the party Constituti on a nd party rules, series of spee ches ca n make proper effect. Party ca dres to "two" lea d by example, t o lead by example we must cha nge our mind, re cog nizi ng that "two" is importa nt. First, learn the Comm unist Party Constitution Party rul es, lear ning lear ning s eries important s pee ch by General Se cretary ca n enhance the ory. With t he "third revol ution" the rise of rapid change s in our life are feeling, t he Communist s shoul d adhere to the t heory of confidence will continue to learn from the voices of the times , the times, in turn, will have ne w requirements for lea ding pa rty cadre s. "Two" is the m ost bas ic meani ng of members all masteri ng the core theory a nd the m ost adva nce d wea pons the ory, compl ement the spirit of cal ci um. Secondl y, the Communist Party Constit ution Party rule s, learni ng lear ning seri es im portant s pee ch by General Se cretary be a ble to firmly buil d the i deol ogical foundation. Under t he impa ct of multiple val ues, t he "two" is to help c ultivate indepe ndent judgment in numer ous mis cella neous multi ple concept s, s o that the majority conse nsus of party member s, the imp ortant magic we apon of the party with the resonance frequency. Fi nally, t he Constit ution of the Communi st Party, party rules, l earni ng learni ng serie s importa nt spe ech can stand crow ds, G eneral Se cretary position. Now, some gras s-roots w ork in the "the old way di dn't w ork, har d way cannot, t he ne w approach would not" phenomenon, sometimes due to a mas s of party member s and cadre s not understa ndi ng, does not meet. I n fact, the mass "convi nci ng" and "ide ntity"Be hind are likely to be party members a nd lea ding cadre s themselve s ig noring beliefs held, re sulting i n lack of pers uasi on and se nse of identit y. "Two" is in fact guaranteed party ca dres w ork, an important prere qui site for convincing the masse s. Ba con sai d it well: "pra ctical men can handle individ ual matters, but looki ng at the w hole operati on gl oball y, but only ma n can do to k nowl edge. "Giving up" two "effective, must first raise awarene ss of lea ding cadres of party members, a s party members l earn real re sponsi bility" to know "to" music "," good " cha nges, i n parallel wit h the ground, do not forget to also a nswer the antenna, draw catches on meteor olog y, whi ch sit betwee n heave n and Earth w hich melds t ogether the dreams of practici ng Communist . Member s cadre s shoul d in "two l earn a do" in the base d post do contribution in all member s in the carrie d out "lear n Constituti on Party rule s, and l earn ser ies s pee ch, do qualified mem bers" learni ng educati on, t his is foll owing party of mass line educati on pra ctice a ctivities a nd "three stri ct three real" topic e ducation zhi hou, de epe ning party education of and once important pra ctice , is pr omoted "three strict three real" topic e ducatio n from "key minority" to all members expand, and from conce ntrated e ducati on t o regular e ducation exte nds of important i nitiatives. Vast numbers of party members and ca dres in t he cours e of two, s hould be

高中数学讲义
kπ ? ,k ? Z ? . 2 ?

①函数 y ? sin 4 x ? cos4 x 的最小正周期是 π . ②终边在 y 轴上的角的集合是 ? a | a ?
? ?

③在同一坐标系中,函数 y ? sin x 的图象和函数 y ? x 的图象有三个公共点. ④把函数 y ? 3sin ? 2 x ? ? 的图象向右平移 3
? ? ? π? ? ? ? π?

π 得到 y ? 3sin 2 x 的图象. 6

⑤函数 y ? sin ? x ? ? 在 ? 0 ,π ? 上是减函数. 2 其中真命题的序号是 . (写出所有正确命题的编号) .

【例13】 对于四面体 ABCD ,下列命题正确的是 ①相对棱 AB 与 CD 所在的直线是异面直线;

②由顶点 A 作四面体的高,其垂足是 ?BCD 的三条高线的交点; ③若分别作 ?ABC 和 ?ABD 的边 AB 上的高,则这两条高所在的直线异面; ④分别作三组相对棱中点的连线,所得的三条线段相交于一点; ⑤最长棱必有某个端点,由它引出的另两条棱的长度之和大于最长棱.
【例14】 设 ? 和 ? 为不重合的两个平面,给出下列命题:

①若 ? 内的两条相交直线分别平行于 ? 内的两条直线,则 ? 平行于 ? ; ②若 ? 外一条直线 l 与 ? 内的一条直线平行,则 l 和 ? 平行; ③设 ? 和 ? 相交于直线 l ,若 ? 内有一条直线垂直于 l ,则 ? 和 ? 垂直; ④直线 l 与 ? 垂直的充分必要条件是 l 与 ? 内的两条直线垂直. 上面命题中,真命题的序号是 ____ . (写出所有真命题的序号)
【例15】 若 x ? ? 2,5? 和 x ??x | x ? 1或x ? 4? 都是假命题,则 x 的范围是___________.

a ?V ,记 a 的象为 f (a ) .若 【例16】 设 V 是已知平面 M 上所有向量的集合,对于映射 f : V ? V ,

? 都有 f (? a ? ?b) ? ? f (a) ? ? f (b) , 映射 f : V ? V 满足: 对所有 a , 则f b ?V 及任意实数 ? ,
称为平面 M 上的线性变换.现有下列命题: ①设 f 是平面 M 上的线性变换,则 f (0) ? 0 ; ②对 a ? V ,设 f (a) ? 2a ,则 f 是平面 M 上的线性变换;w.w.w.k.s.5.u.c.o.m ③若 e 是平面 M 上的单位向量,对 a ? V 设 f (a) ? a ? e ,则 f 是平面 M 上的线性变换; ④设 f 是平面 M 上的线性变换, a , b ?V ,若 a , b 共线,则 f (a) , f (b) 也共线. 其中真命题是 (写出所有真命题的序号)

base d on t heir act ual, striving t o be "lear ning" and "done" markers. Strengthe ning theoretical study, belief and faith. The ory is an a ction gui de, o nly the oretical k nowl edge i n pla ce, to unity, a ction ca n cons ciousl y. Constit ution i s the fundame ntal law of the party, party rules are party must follow t he Ge neral rule s. Studyi ng and impleme nting the party Constituti on Party rules a nd a s eries of importa nt s pee ch, G eneral Se cretary, is a g uide t o persi sting and dev eloping s ociali sm with Chinese characteri stics, i s a ba sic w ork of strengtheni ng the party's construction, but also e ach and every Com munist Party Mem ber's obligations and s olemn res ponsi bility. T hes e important content, for ea ch part y, must k now w oul d believ e will do bot h. We General Secretary of the party Constituti on, a series of remarks with, a nd hold, gra sp the re al "learning" that basis , bas ed on the Constitution s peak to issue, i n accor dance with t he serie s change d the pr obl em. Second, dis cipli ne d in line, to be come la w-a bidi ng mode l. Is not no rule s. If there is no iron di sci pline , party members a nd cadre s will be come a mes s, it will lose its fighting stre ngth 余 有 刃 游 幄 帷 筹 运 中 在 能 定 就 把 确 准 质 本 看 解 理 彻 透 、 析 分 真 认 只 但 终 始 程 过 试 和 习 学 于 穿 贯 它 。 握 掌 难 较 也 , 一 之 点 要 重 的 英 考 高 年 历 是 词 动 语 谓 非 and vitality, purity a nd nat urally much les s advance d. By "two" educati on, party members a nd ca dres to ke ep the "bottom line", not the m ore "red line s", cons ciously pra ctice the "three Suns" and cons ciously act a ccordi ng to the Constitution, party r ules, remai ns a political for ce, t o perfor m party oath, a tree of its own image. T hree is t he loyal, dare to play a nd play to party members . Lear ning i s the Fo undation, is the key to development is the goal. "Two" main obje ctive is to let t he majority of the play to the exempl ary role of party members and ca dres, party Constituti on, party rules to examine . To use new criteri a to gui de our be havior. T hrough e duca tion, the i deal and convi ction, keep in mi nd that membershi p, lear n, learn, learn g o play a vang uard and exemplary rol e, the courag e t o play as, a nd alway s maintain t he pi onee r, pi one ering a nd e nterprisi ng spirit , and const antly improve our ow n ca pacity a nd level of service , accordi ng to positi ons a nd make contri buti ons . Hearts cha nge, lea d more strict "bega n in the know, k now a s Luke Skywalker", "two" activitie s, be qualifie d party member s bot h a starting point a nd e ndi ng point. Party cadres only opinions, Foundati on, Constituti on Party r ules, s eries to better address outsi de in sha pe, "two" this i s State, leadi ng by example, to l ead by exampl e to be qualifie d party member s in the process of doi ng the deep a nd soli d, hig her and more stringe nt. Jobs with new ski lls. To be a qualifie d party membe r, most basic element is alway s adva nce d requirements t hemselves , usi ng their power t o push forwar d the ca use of the part y, the people and the nation. Is t o the lea ding cadres of party members, first of all is base d on the job, do the people i n the heart. T here is not a sl ogan, but aims to better serve the pe ople, targete d efforts to incre ase t he capacity

思维的发掘

能力的飞跃

3

leading cadre s ' awarene ss of right i n pla ce, study the party Constituti on a nd party rules, series of spee ches ca n make proper effect. Party ca dres to "two" lea d by example, t o lead by example we must cha nge our mind, re cog nizi ng that "two" is importa nt. First, learn the Comm unist Party Constitution Party rul es, lear ning lear ning s eries important s pee ch by General Se cretary ca n enhance the ory. With t he "third revol ution" the rise of rapid change s in our life are feeling, t he Communist s shoul d adhere to the t heory of confidence will continue to learn from the voices of the times , the times, in turn, will have ne w requirements for lea ding party cadre s. "Two" is the m ost bas ic meani ng of members all masteri ng the core theory a nd the m ost adva nce d wea pons the ory, compl ement the spirit of cal ci um. Secondl y, the Communist Party Constit ution Party rule s, learni ng lear ning seri es im portant s pee ch by General Se cretary be a ble to firmly buil d the i deol ogical foundation. Under t he impa ct of multiple val ues, t he "two" is to help cultivate indepe ndent judgment in numer ous mis cella neous multi ple concept s, s o that the majority conse nsus of party member s, the important magic we apon of the party with the resonance frequency. Fi nally, t he Constit ution of the Communi st Party, party rules, l earni ng learni ng serie s importa nt spe ech can stand crow ds, G eneral Se cretary position. Now, some gras s-roots w ork in the "the old way di dn't w ork, har d way cannot, t he ne w approach would not" phenomenon, sometimes due to a mas s of par ty member s and cadre s not understa ndi ng, does not meet. I n fact, the mass "convi nci ng" and "ide ntity"Be hind are likely to be party members a nd lea ding cadre s themselve s ig noring beliefs held, re sulting i n lack of pers uasi on and se nse of identit y. "Two" is in fact guaranteed party ca dres w ork, an important prere qui site for convincing the masse s. Ba con sai d it well: "pra ctical men can handle individual matters, but looki ng at the w hole operati on gl oball y, but only ma n can do to k nowl edge. "Giving up" two "e ffective, must first raise awarene ss of lea ding cadres of party members, a s party members l earn real re sponsi bility" to know "to" music "," good "cha nges, i n parallel wit h the ground, do not forget to also a nswer the antenna, draw catches on meteor olog y, whi ch sit betwee n heave n and Earth w hich melds t ogether the dreams of practici ng Communist . Member s cadre s shoul d in "two l earn a d o" in the base d post do contribution in all member s in the carrie d out "lear n Constituti on Party rule s, and l earn ser ies s pee ch, do qualified mem bers" learni ng educati on, t his is foll owing party of mass line educati on pra ctice a ctivities a nd "three stri ct three real" topic e ducation zhi hou, de epe ning party education of and once important pra ctice , is pr omoted "three strict three real" topic e ducation from "key minority" to all members expand, and from conce ntrated e ducati on t o regular e ducation exte nds of important i nitiatives. Vast numbers of party members and ca dres in t he cours e of two, s hould be

高中数学讲义

x 【例17】 设有两个命题: p : 不等式 | x | ? | x ? 1|? a 的解集为 R ,命题 q : f ( x) ? ?(7 ? 3a) 在 R 上

为减函数.如果两个命题中有且只有一个是真命题,那么实数 a 的取值范围 是 .
2

【例18】 关于 x 的方程 ? x 2 ? 1? ? x 2 ? 1 ? k ? 0 ,给出下列四个命题:

①存在实数 k ,使得方程恰有 2 个不同的实根; ②存在实数 k ,使得方程恰有 4 个不同的实根; ③存在实数 k ,使得方程恰有 5 个不同的实根; ④存在实数 k ,使得方程恰有 8 个不同的实根; 其中假 命题的个数是( ) . A. 0 B. 1 C. 2 D. 3

y2 ) ,定义它们之间的一种“距离”: y1 ) 、 B( x2 , 【例19】 对于直角坐标平面内的任意两点 A( x1 ,

AB ? x1 ? x2 ? y1 ? y2 .给出下列三个命题:

①若点 C 在线段 AB 上,则 AC ? CB ? AB ; ②在 ?ABC 中,若 ?C ? 90? ,则 AC ? CB ? AB ; ③在 ?ABC 中, AC ? CB ? AB . 其中真命题的个数为( A. 1 个 B. 2 个 ) C. 3 个 D. 4 个
2 2 2

【例20】 设直线系 M : x cos? ? ( y ? 2)sin ? ? 1 (0 ≤ ? ≤ 2π) ,对于下列四个命题:

A. M 中所有直线均经过一个定点 B.存在定点 P 不在 M 中的任一条直线上 C.对于任意整数 n(n ≥ 3) ,存在正 n 边形,其所有边均在 M 中的直线上 D. M 中的直线所能围成的正三角形面积都相等 其中真命题的代号是 (写出所有真命题的代号) .

题型二:四种命题之间的关系
【例21】 命题“若 x ? y ,则 | x |?| y | ”,写出它的逆命题、否命题、逆否命题,并判断它们的真假
王新敞
奎屯 新疆

【例22】 写出命题“若 a , b 都是偶数,则 a ? b 是偶数”的逆命题,否命题,逆否命题,并判断它们的

真假.
【例23】 写出下列命题的逆命题,否命题,逆否命题,并判断它们的真假.

⑴“负数的平方是正数”;

4

base d on t heir act ual, striving t o be "lear ning" and "done" markers. Strengthe ning theoretical study, belief and faith. The ory is an a ction gui de, only the oretical k nowl edge i n pla ce, to unity, a ction ca n cons ciousl y. Constit ution i s the fundame ntal law of the party, party rules are party must follow t he Ge neral rule s. St udyi ng and impleme nting the party Constituti on Party rules a nd a s eries of important s pee ch, G eneral Se cretary, is a g uide t o persi sting and dev eloping s ociali sm with Chinese characteri stics, i s a ba sic w ork of strengtheni ng the party's construction, but also e ach and every Com munist Party Mem ber's obligations and s olemn res ponsi bility. T hes e important content, for ea ch part y, must k now w oul d believ e will do bot h. We General Secretary of the party Constituti on, a series of remarks with, a nd hold, gra sp the re al "learning" that basis , bas ed on the Constitution s peak to issue, i n accor dance with t he serie s change d the pr obl em. Second, dis cipli ne d in line, to be come la w-a bidi ng mode l. Is not no rule s. If there is no iron di sci pline , party members a nd cadre s will be com e a mes s, it will lose its fighting stre ngth 余 有 刃 游 幄 帷 筹 运 中 在 能 定 就 把 确 准 质 本 看 解 理 彻 透 、 析 分 真 认 只 但 终 始 程 过 试 和 习 学 于 穿 贯 它 。 握 掌 难 较 也 , 一 之 点 要 重 的 英 考 高 年 历 是 词 动 语 谓 非 and vitality, purity a nd nat urally much les s advance d. By "two" educati on, party members a nd ca dres to ke ep the "bottom line", not the m ore "red line s", cons ciously pra ctice the "three Suns" and cons ciously act a ccordi ng to the Constitution, party r ules, remai ns a political for ce, to perfor m party oath, a tree of its own image. T hr ee is t he loyal, dare to play a nd play to party members . Lear ning i s the Foundation, is the key to development is the goal. " Two" main obje ctive is to let t he majority of the play to the exempl ary role of party members and ca dres, party Constituti on, party rules to examine . To use new criteri a to gui de our be havior. T hrough e ducation, the i deal and convi ction, keep in mi nd that m embershi p, lear n, learn, learn g o play a vang uard and exemplary rol e, the courage t o play as, a nd alway s maintain t he pi onee r, pi one ering a nd e nterprisi ng spirit , and const antly improve our ow n ca pacity a nd level of service , accordi ng to positi ons a nd mak e contri buti ons . Hearts cha nge, lea d more strict "bega n in the know, k now a s Luke Skywalker", "two" activitie s, be qualifie d party member s bot h a starting point a nd e ndi ng point. Party cadres only opinions, Foundati on, Constituti on Party r ules, s eries to better address outsi de in sha pe, "two" this i s State, leadi ng by example, to l ead by exampl e to be qualifie d party member s in the process of doi ng the deep a nd soli d, hig her and more stringe nt. Jobs with new ski lls. To be a qualifie d party membe r, most ba sic element is alway s adva nce d requirements t hemselves , usi ng their power t o push forwar d the ca use of the part y, the people and the nation. Is t o the lea ding cadres of party members, first of all is base d on the job, do the people i n the heart. T here is not a sl ogan, but aims to better serve the pe ople, targete d efforts to incre ase the capacity

思维的发掘

能力的飞跃

leading cadre s ' awarene ss of right i n pla ce, study the party Constituti on a nd party rules, series of spee ches ca n make proper effect. Party ca dres to "two" lea d by example, t o lead by example we must cha nge our mind, re cog nizi ng that "two" is importa nt. First, learn the Comm unist Party Constitution Party rul es, lear ning lear ning s eries important s pee ch by General Se cretary ca n enhance the ory. With t he "third revol ution" the rise of rapid change s in our life are feeling, t he Communist s shoul d adhere to the t heory of confidence will continue to learn from the voices of the times , the times, in turn, will have ne w requirements for lea ding pa rty cadre s. "Two" is the m ost bas ic meani ng of members all masteri ng the core theory a nd the m ost adva nce d wea pons the ory, compl ement the spirit of cal ci um. Secondl y, the Communist Party Constit ution Party rule s, learni ng lear ning seri es im portant s pee ch by General Se cretary be a ble to firmly buil d the i deol ogical foundation. Under t he impa ct of multiple val ues, t he "two" is to help c ultivate indepe ndent judgment in numer ous mis cella neous multi ple concept s, s o that the majority conse nsus of party member s, the imp ortant magic we apon of the party with the resonance frequency. Fi nally, t he Constit ution of the Communi st Party, party rules, l earni ng learni ng serie s importa nt spe ech can stand crow ds, G eneral Se cretary position. Now, some gras s-roots w ork in the "the old way di dn't w ork, har d way cannot, t he ne w approach would not" phenomenon, sometimes due to a mas s of party member s and cadre s not understa ndi ng, does not meet. I n fact, the mass "convi nci ng" and "ide ntity"Be hind are likely to be party members a nd lea ding cadre s themselve s ig noring beliefs held, re sulting i n lack of pers uasi on and se nse of identit y. "Two" is in fact guaranteed party ca dres w ork, an important prere qui site for convincing the masse s. Ba con sai d it well: "pra ctical men can handle individ ual matters, but looki ng at the w hole operati on gl oball y, but only ma n can do to k nowl edge. "Giving up" two "effective, must first raise awarene ss of lea ding cadres of party members, a s party members l earn real re sponsi bility" to know "to" music "," good " cha nges, i n parallel wit h the ground, do not forget to also a nswer the antenna, draw catches on meteor olog y, whi ch sit betwee n heave n and Earth w hich melds t ogether the dreams of practici ng Communist . Member s cadre s shoul d in "two l earn a do" in the base d post do contribution in all member s in the carrie d out "lear n Constituti on Party rule s, and l earn ser ies s pee ch, do qualified mem bers" learni ng educati on, t his is foll owing party of mass line educati on pra ctice a ctivities a nd "three stri ct three real" topic e ducation zhi hou, de epe ning party education of and once important pra ctice , is pr omoted "three strict three real" topic e ducatio n from "key minority" to all members expand, and from conce ntrated e ducati on t o regular e ducation exte nds of important i nitiatives. Vast numbers of party members and ca dres in t he cours e of two, s hould be

高中数学讲义

⑵“若 a 和 b 都是偶数,则 a ? b 是偶数”; ⑶“当 c ? 0 时,若 a ? b ,则 ac ? bc ”; ⑷“若 x ? y ? 5 ,则 x ? 3 且 y ? 2 ”;
【例24】 写出下列命题的否命题,并判断否命题的真假.

⑴命题 p :“若 ac ? 0, 则二次方程 ax 2 ? bx ? c ? 0 没有实根”; ⑵命题 q :“若 x ? a 且 x ? b ,则 x2 ? (a ? b) x ? ab ? 0 ”; ⑶命题 r :“若 ( x ? 1)( x ? 2) ? 0 ,则 x ? 1 或 x ? 2 ”. ⑷命题 l :“ ?ABC 中,若 ?C ? 90? ,则 ?A 、 ?B 都是锐角”; b, c 中至少有一个为零”. ⑸命题 s :“若 abc ? 0 ,则 a ,
【例25】 如果两个三角形全等,那么它们的面积相等; 如果两个三角形的面积相等,那么它们全等;

如果两个三角形不全等,那么它们的面积不相等; 如果两个三角形的面积不相等,那么它们不全等; 命题②、③、④与命题①有何关系?

① ② ③ ④

【例26】 下列命题中正确的是(
2 2



①“若 x ? y ? 0 ,则 x , y 不全为零”的否命题 ②“正多边形都相似”的逆命题 ③“若 m ? 0 ,则 x 2 ? x ? m ? 0 有实根”的逆否命题 ④“若 x ? 3 是有理数,则 x 是无理数”的逆否命题 A.①②③④ B.①③④ C.②③④ D.①④ )

b ? R) ,则“ a ? b ? 0 ”的逆否命题是( 【例27】 命题:“若 a2 ? b2 ? 0(a ,
b ? R) ,则 a 2 ? b2 ? 0 A.若 a ? b ? 0(a ,
b ? R) ,则 a 2 ? b2 ? 0 B.若 a ? 0 且 b ? 0(a ,
b ? R) ,则 a 2 ? b2 ? 0 C.若 a ? b ? 0(a ,

b ? R) ,则 a 2 ? b2 ? 0 D.若 a ? 0 或 b ? 0(a ,

【例28】 命题:“若 x 2 ? 1 ,则 ?1 ? x ? 1 ”的逆否命题是(



A.若 x ≥1 ,则 x ≥ 1 或 x ≤ ?1
2

B.若 ?1 ? x ? 1 ,则 x 2 ? 1 D.若 x ≥ 1 或 x ≤ ?1 ,则 x2 ≥1

C.若 x ? 1 或 x ? ?1 ,则 x 2 ? 1

【例29】 已知命题“如果 a ≤1 ,那么关于 x 的不等式 (a2 ? 4) x2 ? (a ? 2) x ? 1≥ 0 的解集为 ? ”.它的

逆命题、否命题、逆否命题及原命题中是假命题的共有( A.0 个 B.2 个 C.3 个

) D.4 个

base d on t heir act ual, striving t o be "lear ning" and "done" markers. Strengthe ning theoretical study, belief and faith. The ory is an a ction gui de, o nly the oretical k nowl edge i n pla ce, to unity, a ction ca n cons ciousl y. Constit ution i s the fundame ntal law of the party, party rules are party must follow t he Ge neral rule s. Studyi ng and impleme nting the party Constituti on Party rules a nd a s eries of importa nt s pee ch, G eneral Se cretary, is a g uide t o persi sting and dev eloping s ociali sm with Chinese characteri stics, i s a ba sic w ork of strengtheni ng the party's construction, but also e ach and every Com munist Party Mem ber's obligations and s olemn res ponsi bility. T hes e important content, for ea ch part y, must k now w oul d believ e will do bot h. We General Secretary of the party Constituti on, a series of remarks with, a nd hold, gra sp the re al "learning" that basis , bas ed on the Constitution s peak to issue, i n accor dance with t he serie s change d the pr obl em. Second, dis cipli ne d in line, to be come la w-a bidi ng mode l. Is not no rule s. If there is no iron di sci pline , party members a nd cadre s will be come a mes s, it will lose its fighting stre ngth 余 有 刃 游 幄 帷 筹 运 中 在 能 定 就 把 确 准 质 本 看 解 理 彻 透 、 析 分 真 认 只 但 终 始 程 过 试 和 习 学 于 穿 贯 它 。 握 掌 难 较 也 , 一 之 点 要 重 的 英 考 高 年 历 是 词 动 语 谓 非 and vitality, purity a nd nat urally much les s advance d. By "two" educati on, party members a nd ca dres to ke ep the "bottom line", not the m ore "red line s", cons ciously pra ctice the "three Suns" and cons ciously act a ccordi ng to the Constitution, party r ules, remai ns a political for ce, t o perfor m party oath, a tree of its own image. T hree is t he loyal, dare to play a nd play to party members . Lear ning i s the Fo undation, is the key to development is the goal. "Two" main obje ctive is to let t he majority of the play to the exempl ary role of party members and ca dres, party Constituti on, party rules to examine . To use new criteri a to gui de our be havior. T hrough e duca tion, the i deal and convi ction, keep in mi nd that membershi p, lear n, learn, learn g o play a vang uard and exemplary rol e, the courag e t o play as, a nd alway s maintain t he pi onee r, pi one ering a nd e nterprisi ng spirit , and const antly improve our ow n ca pacity a nd level of service , accordi ng to positi ons a nd make contri buti ons . Hearts cha nge, lea d more strict "bega n in the know, k now a s Luke Skywalker", "two" activitie s, be qualifie d party member s bot h a starting point a nd e ndi ng point. Party cadres only opinions, Foundati on, Constituti on Party r ules, s eries to better address outsi de in sha pe, "two" this i s State, leadi ng by example, to l ead by exampl e to be qualifie d party member s in the process of doi ng the deep a nd soli d, hig her and more stringe nt. Jobs with new ski lls. To be a qualifie d party membe r, most basic element is alway s adva nce d requirements t hemselves , usi ng their power t o push forwar d the ca use of the part y, the people and the nation. Is t o the lea ding cadres of party members, first of all is base d on the job, do the people i n the heart. T here is not a sl ogan, but aims to better serve the pe ople, targete d efforts to incre ase t he capacity

思维的发掘

能力的飞跃

5

leading cadre s ' awarene ss of right i n pla ce, study the party Constituti on a nd party rules, series of spee ches ca n make proper effect. Party ca dres to "two" lea d by example, t o lead by example we must cha nge our mind, re cog nizi ng that "two" is importa nt. First, learn the Comm unist Party Constitution Party rul es, lear ning lear ning s eries important s pee ch by General Se cretary ca n enhance the ory. With t he "third revol ution" the rise of rapid change s in our life are feeling, t he Communist s shoul d adhere to the t heory of confidence will continue to learn from the voices of the times , the times, in turn, will have ne w requirements for lea ding party cadre s. "Two" is the m ost bas ic meani ng of members all masteri ng the core theory a nd the m ost adva nce d wea pons the ory, compl ement the spirit of cal ci um. Secondl y, the Communist Party Constit ution Party rule s, learni ng lear ning seri es im portant s pee ch by General Se cretary be a ble to firmly buil d the i deol ogical foundation. Under t he impa ct of multiple val ues, t he "two" is to help cultivate indepe ndent judgment in numer ous mis cella neous multi ple concept s, s o that the majority conse nsus of party member s, the important magic we apon of the party with the resonance frequency. Fi nally, t he Constit ution of the Communi st Party, party rules, l earni ng learni ng serie s importa nt spe ech can stand crow ds, G eneral Se cretary position. Now, some gras s-roots w ork in the "the old way di dn't w ork, har d way cannot, t he ne w approach would not" phenomenon, sometimes due to a mas s of par ty member s and cadre s not understa ndi ng, does not meet. I n fact, the mass "convi nci ng" and "ide ntity"Be hind are likely to be party members a nd lea ding cadre s themselve s ig noring beliefs held, re sulting i n lack of pers uasi on and se nse of identit y. "Two" is in fact guaranteed party ca dres w ork, an important prere qui site for convincing the masse s. Ba con sai d it well: "pra ctical men can handle individual matters, but looki ng at the w hole operati on gl oball y, but only ma n can do to k nowl edge. "Giving up" two "e ffective, must first raise awarene ss of lea ding cadres of party members, a s party members l earn real re sponsi bility" to know "to" music "," good "cha nges, i n parallel wit h the ground, do not forget to also a nswer the antenna, draw catches on meteor olog y, whi ch sit betwee n heave n and Earth w hich melds t ogether the dreams of practici ng Communist . Member s cadre s shoul d in "two l earn a d o" in the base d post do contribution in all member s in the carrie d out "lear n Constituti on Party rule s, and l earn ser ies s pee ch, do qualified mem bers" learni ng educati on, t his is foll owing party of mass line educati on pra ctice a ctivities a nd "three stri ct three real" topic e ducation zhi hou, de epe ning party education of and once important pra ctice , is pr omoted "three strict three real" topic e ducation from "key minority" to all members expand, and from conce ntrated e ducati on t o regular e ducation exte nds of important i nitiatives. Vast numbers of party members and ca dres in t he cours e of two, s hould be

高中数学讲义

【例30】 有下列四个命题: ①“若 x ? y ? 0 ,则 x, y 互为相反数”的逆命题;

②“全等三角形的面积相等”的否命题; ③“若 q ≤ 1 ,则 x2 ? 2x ? q ? 0 有实根”的逆否命题; ④“等边三角形的三个内角相等”逆命题; 其中真命题的个数为( ) A. 1 B. 2 C. 3

D. 4

【例31】 下面有四个命题: ① 集合 N 中最小的数是 1 ; ② 若 ?a 不属于 N ,则 a 属于 N ; ③ 若

a ? N , b ? N , 则 a ? b 的最小值为 2 ;④ x 2 ? 1 ? 2 x 的解可表示为 ? 1,1? .其中真命题的个数
为() A. 0 个 B. 1 个 C. 2 个 D. 3 个

【例32】 有下列四个命题:①“若 x ? y ? 0 , 则 x, y 互为相反数”的逆命题;②“全等三角形的面积

相等”的否命题; ③“若 q ? 1 ,则 x2 ? 2x ? q ? 0 有实根”的逆否命题;④“不等边三角形的 三个内角相等”逆命题. 其中真命题为 A.①② B.②③ ( ) D.③④

C.①③

b, c ? R ,若 a ? b ,则 ac 2 ? bc 2 ”以及它的逆命题、否命题、逆否命题中, 【例33】 原命题:“设 a ,

真命题共有( A. 0

)个. B. 1

C. 2

D. 4

【例34】 给出以下四个命题: ①“若 x ? y ? 0 ,则 x , y 互为相反数”的逆命题;

②“全等三角形的面积相等”的否命题; ③“若 q ≤ ?1 ,则 x2 ? x ? q ? 0 有实根”的逆否命题; ④“不等边三角形的三内角相等”的逆否命题. 其中真命题是( ) A.①② B.②③ C.①③
【例35】 命题:“若 x 2 ? 1 ,则 ?1 ? x ? 1 ”的逆否命题是(

D.③④



A.若 x ≥1 ,则 x ≥ 1 或 x ≤ ?1
2

B.若 ?1 ? x ? 1 ,则 x 2 ? 1 D.若 x ≥ 1 或 x ≤ ?1 ,则 x2 ≥1

C.若 x ? 1 或 x ? ?1 ,则 x 2 ? 1

【例36】 有下列四个命题:①“若 x ? y ? 0 ,则 x , y 互为相反数”的逆命题;②“全等三角形的面积相

6

base d on t heir act ual, striving t o be "lear ning" and "done" markers. Strengthe ning theoretical study, belief and faith. The ory is an a ction gui de, only the oretical k nowl edge i n pla ce, to unity, a ction ca n cons ciousl y. Constit ution i s the fundame ntal law of the party, party rules are party must follow t he Ge neral rule s. St udyi ng and impleme nting the party Constituti on Party rules a nd a s eries of important s pee ch, G eneral Se cretary, is a g uide t o persi sting and dev eloping s ociali sm with Chinese characteri stics, i s a ba sic w ork of strengtheni ng the party's construction, but also e ach and every Com munist Party Mem ber's obligations and s olemn res ponsi bility. T hes e important content, for ea ch part y, must k now w oul d believ e will do bot h. We General Secretary of the party Constituti on, a series of remarks with, a nd hold, gra sp the re al "learning" that basis , bas ed on the Constitution s peak to issue, i n accor dance with t he serie s change d the pr obl em. Second, dis cipli ne d in line, to be come la w-a bidi ng mode l. Is not no rule s. If there is no iron di sci pline , party members a nd cadre s will be com e a mes s, it will lose its fighting stre ngth 余 有 刃 游 幄 帷 筹 运 中 在 能 定 就 把 确 准 质 本 看 解 理 彻 透 、 析 分 真 认 只 但 终 始 程 过 试 和 习 学 于 穿 贯 它 。 握 掌 难 较 也 , 一 之 点 要 重 的 英 考 高 年 历 是 词 动 语 谓 非 and vitality, purity a nd nat urally much les s advance d. By "two" educati on, party members a nd ca dres to ke ep the "bottom line", not the m ore "red line s", cons ciously pra ctice the "three Suns" and cons ciously act a ccordi ng to the Constitution, party r ules, remai ns a political for ce, to perfor m party oath, a tree of its own image. T hr ee is t he loyal, dare to play a nd play to party members . Lear ning i s the Foundation, is the key to development is the goal. " Two" main obje ctive is to let t he majority of the play to the exempl ary role of party members and ca dres, party Constituti on, party rules to examine . To use new criteri a to gui de our be havior. T hrough e ducation, the i deal and convi ction, keep in mi nd that m embershi p, lear n, learn, learn g o play a vang uard and exemplary rol e, the courage t o play as, a nd alway s maintain t he pi onee r, pi one ering a nd e nterprisi ng spirit , and const antly improve our ow n ca pacity a nd level of service , accordi ng to positi ons a nd mak e contri buti ons . Hearts cha nge, lea d more strict "bega n in the know, k now a s Luke Skywalker", "two" activitie s, be qualifie d party member s bot h a starting point a nd e ndi ng point. Party cadres only opinions, Foundati on, Constituti on Party r ules, s eries to better address outsi de in sha pe, "two" this i s State, leadi ng by example, to l ead by exampl e to be qualifie d party member s in the process of doi ng the deep a nd soli d, hig her and more stringe nt. Jobs with new ski lls. To be a qualifie d party membe r, most ba sic element is alway s adva nce d requirements t hemselves , usi ng their power t o push forwar d the ca use of the part y, the people and the nation. Is t o the lea ding cadres of party members, first of all is base d on the job, do the people i n the heart. T here is not a sl ogan, but aims to better serve the pe ople, targete d efforts to incre ase the capacity

思维的发掘

能力的飞跃

leading cadre s ' awarene ss of right i n pla ce, study the party Constituti on a nd party rules, series of spee ches ca n make proper effect. Party ca dres to "two" lea d by example, t o lead by example we must cha nge our mind, re cog nizi ng that "two" is importa nt. First, learn the Comm unist Party Constitution Party rul es, lear ning lear ning s eries important s pee ch by General Se cretary ca n enhance the ory. With t he "third revol ution" the rise of rapid change s in our life are feeling, t he Communist s shoul d adhere to the t heory of confidence will continue to learn from the voices of the times , the times, in turn, will have ne w requirements for lea ding pa rty cadre s. "Two" is the m ost bas ic meani ng of members all masteri ng the core theory a nd the m ost adva nce d wea pons the ory, compl ement the spirit of cal ci um. Secondl y, the Communist Party Constit ution Party rule s, learni ng lear ning seri es im portant s pee ch by General Se cretary be a ble to firmly buil d the i deol ogical foundation. Under t he impa ct of multiple val ues, t he "two" is to help c ultivate indepe ndent judgment in numer ous mis cella neous multi ple concept s, s o that the majority conse nsus of party member s, the imp ortant magic we apon of the party with the resonance frequency. Fi nally, t he Constit ution of the Communi st Party, party rules, l earni ng learni ng serie s importa nt spe ech can stand crow ds, G eneral Se cretary position. Now, some gras s-roots w ork in the "the old way di dn't w ork, har d way cannot, t he ne w approach would not" phenomenon, sometimes due to a mas s of party member s and cadre s not understa ndi ng, does not meet. I n fact, the mass "convi nci ng" and "ide ntity"Be hind are likely to be party members a nd lea ding cadre s themselve s ig noring beliefs held, re sulting i n lack of pers uasi on and se nse of identit y. "Two" is in fact guaranteed party ca dres w ork, an important prere qui site for convincing the masse s. Ba con sai d it well: "pra ctical men can handle individ ual matters, but looki ng at the w hole operati on gl oball y, but only ma n can do to k nowl edge. "Giving up" two "effective, must first raise awarene ss of lea ding cadres of party members, a s party members l earn real re sponsi bility" to know "to" music "," good " cha nges, i n parallel wit h the ground, do not forget to also a nswer the antenna, draw catches on meteor olog y, whi ch sit betwee n heave n and Earth w hich melds t ogether the dreams of practici ng Communist . Member s cadre s shoul d in "two l earn a do" in the base d post do contribution in all member s in the carrie d out "lear n Constituti on Party rule s, and l earn ser ies s pee ch, do qualified mem bers" learni ng educati on, t his is foll owing party of mass line educati on pra ctice a ctivities a nd "three stri ct three real" topic e ducation zhi hou, de epe ning party education of and once important pra ctice , is pr omoted "three strict three real" topic e ducatio n from "key minority" to all members expand, and from conce ntrated e ducati on t o regular e ducation exte nds of important i nitiatives. Vast numbers of party members and ca dres in t he cours e of two, s hould be

高中数学讲义

等”的否命题;③“若 q ≤ 1 ,则 x2 ? 2x ? q ? 0 有实根”的逆否命题;④“不等边三角形的三个 内角相等”逆命题.其中真命题为( A.①② B.②③ ) C.①③

D.③④ .

【例37】 命题“若 ?ABC 不是等腰三角形,则它的任何两个内角不相等”的逆否命题是 【例38】 下列命题中_________为真命题. ①“ A B ? A ”成立的必要条件是“ A ? B ”;

②“若 x2 ? y 2 ? 0 ,则 x , y 全为 0 ”的否命题; ③“全等三角形是相似三角形”的逆命题; ④“圆内接四边形对角互补”的逆否命题.
【例39】 “在 ?ABC 中,若 ?C ? 90? ,则 ?A 、 ?B 都是锐角”的否命题为



【例40】 有下列四个命题:①命题“若 xy ? 1 ,则 x , y 互为倒数”的逆命题;②命题“面积相等的三

角形全等”的否命题;③命题“若 m ≤ 1 ,则 x 2 ? 2 x ? m ? 0 有实根”的逆否命题;④命题“若
A B ? B ,则 A ? B ”的逆否命题.

其中是真命题的是

(填上你认为正确的命题的序号) .

【例41】 命题“若 x, y 是奇数,则 x ? y 是偶数”的逆否命题是

;它是

命题.

【例42】 写出命题“若 m ? 0 ,则方程 x ? x ? m ? 0 有实数根”的逆否命题,判断其真假,并加以证
2

明.

【例43】 已知等比数列 {an } 的前 n 项和为 Sn .

⑴若 Sm , Sm ? 2 , S m ?1 成等差数列,证明 am , am ? 2 , am ?1 成等差数列; ⑵写出⑴的逆命题,判断它的真伪,并给出证明.

【例44】 在平面直角坐标系 xOy 中,直线 l 与抛物线 y ? 2 x 相交于 A、B 两点.
2

(1)求证:“如果直线 l 过点 T(3,0) ,那么 OA ? OB =3”是真命题; (2)写出(1)中命题的逆命题,判断它是真命题还是假命题,并说明理由.

?? ?

?? ?

base d on t heir act ual, striving t o be "lear ning" and "done" markers. Strengthe ning theoretical study, belief and faith. The ory is an a ction gui de, o nly the oretical k nowl edge i n pla ce, to unity, a ction ca n cons ciousl y. Constit ution i s the fundame ntal law of the party, party rules are party must follow t he Ge neral rule s. Studyi ng and impleme nting the party Constituti on Party rules a nd a s eries of importa nt s pee ch, G eneral Se cretary, is a g uide t o persi sting and dev eloping s ociali sm with Chinese characteri stics, i s a ba sic w ork of strengtheni ng the party's construction, but also e ach and every Com munist Party Mem ber's obligations and s olemn res ponsi bility. T hes e important content, for ea ch part y, must k now w oul d believ e will do bot h. We General Secretary of the party Constituti on, a series of remarks with, a nd hold, gra sp the re al "learning" that basis , bas ed on the Constitution s peak to issue, i n accor dance with t he serie s change d the pr obl em. Second, dis cipli ne d in line, to be come la w-a bidi ng mode l. Is not no rule s. If there is no iron di sci pline , party members a nd cadre s will be come a mes s, it will lose its fighting stre ngth 余 有 刃 游 幄 帷 筹 运 中 在 能 定 就 把 确 准 质 本 看 解 理 彻 透 、 析 分 真 认 只 但 终 始 程 过 试 和 习 学 于 穿 贯 它 。 握 掌 难 较 也 , 一 之 点 要 重 的 英 考 高 年 历 是 词 动 语 谓 非 and vitality, purity a nd nat urally much les s advance d. By "two" educati on, party members a nd ca dres to ke ep the "bottom line", not the m ore "red line s", cons ciously pra ctice the "three Suns" and cons ciously act a ccordi ng to the Constitution, party r ules, remai ns a political for ce, t o perfor m party oath, a tree of its own image. T hree is t he loyal, dare to play a nd play to party members . Lear ning i s the Fo undation, is the key to development is the goal. "Two" main obje ctive is to let t he majority of the play to the exempl ary role of party members and ca dres, party Constituti on, party rules to examine . To use new criteri a to gui de our be havior. T hrough e duca tion, the i deal and convi ction, keep in mi nd that membershi p, lear n, learn, learn g o play a vang uard and exemplary rol e, the courag e t o play as, a nd alway s maintain t he pi onee r, pi one ering a nd e nterprisi ng spirit , and const antly improve our ow n ca pacity a nd level of service , accordi ng to positi ons a nd make contri buti ons . Hearts cha nge, lea d more strict "bega n in the know, k now a s Luke Skywalker", "two" activitie s, be qualifie d party member s bot h a starting point a nd e ndi ng point. Party cadres only opinions, Foundati on, Constituti on Party r ules, s eries to better address outsi de in sha pe, "two" this i s State, leadi ng by example, to l ead by exampl e to be qualifie d party member s in the process of doi ng the deep a nd soli d, hig her and more stringe nt. Jobs with new ski lls. To be a qualifie d party membe r, most basic element is alway s adva nce d requirements t hemselves , usi ng their power t o push forwar d the ca use of the part y, the people and the nation. Is t o the lea ding cadres of party members, first of all is base d on the job, do the people i n the heart. T here is not a sl ogan, but aims to better serve the pe ople, targete d efforts to incre ase t he capacity

思维的发掘

能力的飞跃

7



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