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 . 求下列每对集合的交集:
(1)
,
;
(2)
,
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ffc2628f0e121bba72f752c55be44fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01f2a0c24fdba86066b2dbfc89ff44aa.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5267cc758a566c5ec857638a7ed9f11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fd665d9e145bd702a2667dae9c6191.png)
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4 . 求下列集合的并集:
(1)
,
;
(2)
,
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f88506628ea3a6dbf27ce97bf87442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b5fd68b43a19d5932eaeb525a70110.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ed54e6f925630492cb446ac78cb5bd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/714126aeb68ea8255c97c08c0d4a1393.png)
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5 . 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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6 . 判断下列命题是否正确.
(1)集合
与集合
表示同一集合;( )
(2)集合
与集合
表示同一集合;( )
(3)集合
与集合
不表示同一集合;( )
(4)集合
与集合
表示同一集合.( )
(1)集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/996302ec6009fab54792bca99fbd3e5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21498c5c0cdd56468b648ef486f5258e.png)
(2)集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e69fa1e13251871635f4adf2945f311.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7403e3b8711e1c53efc2086f7058b27.png)
(3)集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ea8cd1f32f11c197adc4393fac77a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7cc85485bc64e75829b812bcae5be6a.png)
(4)集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1030e0fb695cade79bb60748765aa51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/975500b05339f422cca2978f47122a38.png)
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