1 . 已知命题
.
(1)写出命题
的否定;
(2)判断命题
的真假,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab535cb68c6a03152976712ea5ccb1aa.png)
(1)写出命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)判断命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
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2 . 写出下列命题的否定,并判断命题的否定的真假.
(1)
,
;
(2)有一个素数是偶数;
(3)任意两个三角形的底边长和底边对应的高的长度相等,那么这两个三角形相似.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c81b0ac874f65acbdd37b3ca55467713.png)
(2)有一个素数是偶数;
(3)任意两个三角形的底边长和底边对应的高的长度相等,那么这两个三角形相似.
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名校
3 . 写出下列命题的否定,并判断其真假:
(1)
,方程
必有实根;
(2)
,使得
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44bef5e2df41b92f8aa7319710f79de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac671e6d87de2fb5f7ad3aab582866d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaa0583842bff0b9ac0a539656f88099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3ef6ac3a5f1358143e94eb31f6687d2.png)
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4 . 判断下列命题是全称量词命题还是存在量词命题,写出这些命题的否定.
(1)
,
与3的和不等于0;
(2)
,
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4dbe9afeae563561806eac216ee841f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5e24ce175dd3b1a25dbee402c36c98e.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ccd7af9298cd5ff19d8866fedb42ec4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1597e4dad6d72c336e4a85ab389fa05.png)
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5 . 判断下列全称(存在量词)命题的真假:
(1)
,
;
(2)有些偶数能被
整除;
(3)所有的对角线互相垂直的四边形是菱形;
(4)有些三角形是锐角三角形.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fa139aad70ad1ac124affc3fe5d75c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ffe9ac6ae9ce074dea93e3748a1089c.png)
(2)有些偶数能被
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
(3)所有的对角线互相垂直的四边形是菱形;
(4)有些三角形是锐角三角形.
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6 . 写出下列全称(存在量词)命题的否定:
(1)
,
;
(2)
,
;
(3)存在一个实数,它的绝对值不是正数;
(4)所有的矩形都是正方形.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8645952ea14b25443f411d39bdec641e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/412fb8eef3b94bcaa718f944d53852af.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7fbdd49b17c2e858b4577bb84e401f.png)
(3)存在一个实数,它的绝对值不是正数;
(4)所有的矩形都是正方形.
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解题方法
7 . (1)已知命题
.若
是
的充分不必要条件,求实数
的取值范围;
(2)已知
,命题
;命题
.若
均为真命题,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880ae30b42e7107189eca2a6fcf4a507.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/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3e9e61867519269541b18c41568a301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4cb42904d901fda9b24658242ab451e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
8 . 写出下列命题的否定,并判断其真假:
(1)
;
(2)p:有些三角形的三条边相等;
(3)p:菱形的对角线互相垂直;
(4)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a987ea219a08d4765f70e65b3362f7b9.png)
(2)p:有些三角形的三条边相等;
(3)p:菱形的对角线互相垂直;
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23537fe10207db7b2824c9facc41abd3.png)
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9 . 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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10 . 已知
,命题
,
;命题
,
.
(1)写出命题p的否定
,并求
为真时,实数a的取值范围;
(2)若命题p,q有且只有一个为真,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed8f02a4c4da45108c38df4a2812d09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6626e1dfbbf91023ca25544c21d886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d19de1563ccf0f867f91bc031773053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2b9b4d5eed73c4b4147b5d6c4ec526.png)
(1)写出命题p的否定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffc1bb9d53a27d484396ad74d6a26e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffc1bb9d53a27d484396ad74d6a26e0.png)
(2)若命题p,q有且只有一个为真,求实数a的取值范围.
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