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 . 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 . 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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7 . 判断正误(正确的写正确,错误的写错误)
(1)任何集合至少有两个子集.( )
(2)
.( )
(3)若
,且
,则
.( )
(4)集合
的子集是
,
,
.( )
(1)任何集合至少有两个子集.
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c91b4a4530b820b6728f37e497847faf.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ad78dc8b8aed907b4fe9640c997454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb584b83ae783a0ec8a9b4628b7fca3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(4)集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69dcd9264c20f3413a875633884622db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5f5e5688b5c7e514ee72597690a7676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6170ed4a10e57487d525e71610dff82f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69dcd9264c20f3413a875633884622db.png)
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8 . 判断正误(正确的打“ 正确”,错误的打“ 错误”)
(1)
,
,
.( )
(2)若
,则
.( )
(3)若
,则
或
,二者必居其一.( )
(4)集合
可能成立.( )
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86ce6a27fba0d3dd408cda9ea3f04f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d01497d24da642df2e7b107b610ff21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dfd35183617b8d659a74101420aa310.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5d668dcafd840848827736f1b83b067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b209386eac3bf9eacec0c0514ef0497.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63919cff4d3b194aade6e2b8f9fcac7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde2827722685b8a71f9aae2dc4d7484.png)
(4)集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a986e6afe28d205a596939fbbe189.png)
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9 . 判断正误(正确的写“正确”,错误的写“错误”)
(1)集合中的元素一定是数.( )
(2)参加北京冬奥会闭幕式的全体人员是一个集合.( )
(3)由1,2,3构成的集合与由3,2,1构成的集合是同一个集合.( )
(4)一个集合中可以找到两个相同的元素.( )
(1)集合中的元素一定是数.
(2)参加北京冬奥会闭幕式的全体人员是一个集合.
(3)由1,2,3构成的集合与由3,2,1构成的集合是同一个集合.
(4)一个集合中可以找到两个相同的元素.
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10 . 判断正误(正确的打“√”,错误的打“×”)
(1)一个集合可以表示为
.( )
(2)集合
和
表示同一个集合.( )
(3)集合
与集合
表示同一个集合.( )
(4)集合
与集合
表示同一个集合.( )
(1)一个集合可以表示为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a7797169cbc987ae4322b67236e46c4.png)
(2)集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7298d277abc534fcddc2cb7548010381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84caee4d118542d154ae0eb308aae30e.png)
(3)集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e11126de0a9ee06f6b2c4667ffca28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d0ee6f2a7ed0601ee9e547b2b7305d.png)
(4)集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f40a4c2200c97ee696e747814f6b5315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6b58c8bf5f1ad2cc181268abeb7065.png)
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