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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4 . 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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5 . 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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