1 . 判断下列存在量词命题的真假:
(1)
;
(2)
;
(3)设
是平面上不在同一直线上的三点,在该平面上存在某个点
,使得
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13bf9417afd9a3a568ade8d1e01f6d5.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bffd9bcf67ae8e37be46f29a573792f.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30fc65a72853bd8ac1ad0828270d3baf.png)
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2 . 写出下列含量词命题的否定:
(1)
每一个素数都是奇数;
(2)
所有二次函数的图象都是轴对称图形;
(3)
;
(4)
有的三角形的垂心在其外部;
(5)
有一个小于210的正整数至少有4个质因数.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51441c8788ff11be766766227793246d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce20ef9c08e82df8c7f45bac6dd31d36.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70edb5fbb4ab94ffed70f69fbf86d2d6.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853bd348db38586386c3cfaf9edfde6c.png)
(5)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aada55745ce663ada46f9c8a46ae7e7a.png)
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3 . 从“充分而不必要条件”“必要而不充分条件”“充要条件”和“既不充分又不必要条件”中选择适当的一种填空.
(1)
是
为正数的______ ;
(2)四边形的两对角线相等是该四边形为矩形的______ ;
(3)四边形的一组对边平行且相等是四边形的两组对边分别平行的______ ;
(4)若
,则
是
的______ .
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b87ecc31822d729a45488d803fff4e16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)四边形的两对角线相等是该四边形为矩形的
(3)四边形的一组对边平行且相等是四边形的两组对边分别平行的
(4)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdbf50b34d559607dc5a75c90a72e558.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
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4 . 指出下列命题中使用了什么量词以及量词的作用范围,并把量词用相应的数学符号取代:
(1)对任意正实数
,
;
(2)对某个大于10的正整数
,
.
(1)对任意正实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecda5a59e734151cd588584cabd424fa.png)
(2)对某个大于10的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1186c6b3c9705444ad96dcb1bf6e523.png)
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2023-10-02更新
|
37次组卷
|
2卷引用:湘教版(2019)必修第一册课本例题1.2.3全称量词和存在量词
5 . 常见不等式的性质:
(1)
是
的_______ 条件;
(2)如果
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
____
;
(3)
是
的______ 条件;
(4)如果
,那么![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f384e98d574fa2676d61624285f88188.png)
____
;如果
,那么![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f384e98d574fa2676d61624285f88188.png)
____
;
(5)如果
,那么![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1810555c0c28fe352841322b85bbc6.png)
____
;
(6)如果
,那么![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f384e98d574fa2676d61624285f88188.png)
____
;
(7)如果
,那么![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81baf482546f298ba289d723bc21e0c3.png)
____
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5556dd86322752a457b3a6ba979c80.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30eb197fcbd6cea2230fbf8946fb82cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b50501087390b0c12b427ac564a834e7.png)
(4)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e76ce07edcc26c09544c0bac0e36413e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f384e98d574fa2676d61624285f88188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69225cfdfbc0a9a1ccfdd15c46353b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5aec517ae1f04792179c173bd662d16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f384e98d574fa2676d61624285f88188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69225cfdfbc0a9a1ccfdd15c46353b8f.png)
(5)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa8950fa963eedb948d6a57871478cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1810555c0c28fe352841322b85bbc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d02a08024fd5d4305bc2638b472fa48.png)
(6)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7ad6cf9fb725f7947bddaf3149ba07d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f384e98d574fa2676d61624285f88188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a0aa3929a1e72941a617ec65e2abc66.png)
(7)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81baf482546f298ba289d723bc21e0c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc4dfbd0391dfa1708c793c9fde635f7.png)
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6 . 全称量词命题与存在量词命题的否定
(1)全称量词命题:
的否定为_____________ .
(2)存在量词命题:
的否定为______________ .
(1)全称量词命题:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac25527dadae26e2ff4fe1c24c358a92.png)
(2)存在量词命题:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3668e31d1f1e495e3cbbd78b2b49fefc.png)
您最近一年使用:0次
7 . 存在量词与存在量词命题
(1)短语“存在一个”“至少有一个”在逻辑中通常叫做______ ,用符号__ 表示;
(2)含有_______ 量词的命题叫做存在量词命题,其一般形式为:______
.
(1)短语“存在一个”“至少有一个”在逻辑中通常叫做
(2)含有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34322d6fb1368468b8435d4617d9d9b3.png)
您最近一年使用:0次
8 . 全称量词与全称量词命题
(1)短语“所有的”“任意一个”在逻辑中通常叫做______ ,用符号__ 表示;
(2)含有_______ 量词的命题叫做全称量词命题,其一般形式为:______
.
(1)短语“所有的”“任意一个”在逻辑中通常叫做
(2)含有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34322d6fb1368468b8435d4617d9d9b3.png)
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9 . 四种条件关系:
(1)如果命题“若
,则
”为真命题且“若
,则
”为假命题,那么
是
的___ 条件.
(2)如果命题“若
,则
”为假命题且“若
,则
”为真命题,那么
是
的___ 条件.
(3)如果命题“若
,则
”为真命题且“若
,则
”也为真命题,那么
是
的___ 条件.
(4)如果命题“若
,则
”为假命题且“若
,则
”也为假命题,那么
是
的___ 条件.
(1)如果命题“若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(2)如果命题“若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(3)如果命题“若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(4)如果命题“若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
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10 . 如果命题“若
,则
”为真命题,那么
是
的_____ 条件,且
是
的____ 条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
您最近一年使用:0次