解题方法
1 . 已知集合
,集合
,命题
,命题
,
.
(1)若命题
为假命题,求实数
的取值范围;
(2)若命题
和命题
至少有一个为真命题,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56b754fa81e4266743c32671ef3eaa03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c04f76d8d1d83442cc69ffe725112511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5708f05b0006d21e05160df77ca0ca8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d19de1563ccf0f867f91bc031773053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/886606543383d11a4db8f21ac1e4e3bf.png)
(1)若命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若命题
![](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/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
2 . 已知命题:
为假命题,则实数a的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249619b8d12335cbd59d4c8b792f3b2d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . “
,
恒成立”是“
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad5fe274cfc8da2dacfb65801f344ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ed736c0decc93f86d194dce040f21bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f202b5a52c2d4fb8d45a9256964d732.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不充分也不必要条件 |
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解题方法
4 . 已知集合
,
.
(1)
时,求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
(2)若命题
:“
,
”是真命题,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d64c9f2fb6136d249860e9ebcc6780e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f75c07e180b8a9bf1ee9424651ccab7d.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
(2)若命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/728ca24844243ea9185f6f79c773145b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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5 . 设命题
:“对任意
,
恒成立”.且命题
为真命题.
(1)求实数
的取值集合
;
(2)在(1)的条件下,设非空集合
,若“
”是“
”的充分条件,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9621ae5bac4c82757ba32db13f914b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)在(1)的条件下,设非空集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9fe6c3da8d64094bd0abc2f7efa524a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bd564d9b1740b443e86eedd36184621.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbf3a1aba112698af9af7d37ba8db089.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
6 . 已知命题“
,
”为假命题,则实数a的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdad626ae647fb9af288c3b348293ad4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94d4da23625ec0b3d0e2eef0cf836e1.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 已知
:存在
,
,
:任意
,
.
(1)若
为假命题,求实数
的取值范围;
(2)若
为真,
为假,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f07ad90ca228230b03f12eb48ee0c1d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce7ac38bfa4b72d546e26075168c565.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f754145f648450f9e14cec4b17140a5.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f675824e539f50cec53120959d32e554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f675824e539f50cec53120959d32e554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c13472bf0353e16784a22e1f890fba40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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8 . 命题
:任意
,
成立;命题
:存在
,
+
成立.
(1)若命题
为假命题,求实数
的取值范围;
(2)若命题
和
有且只有一个为真命题,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d609c6e809717c61cbbae6be515a2d35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0a89e3c30f6e4d4c5db4378b05d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b99ea0c026f1ba13accae4b8c355c14.png)
(1)若命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若命题
![](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)
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9 . 设a∈R,命题p:
,
,命题q:
,
(1)若p为真命题,求实数a的取值范围;
(2)若p或q为真命题,p且q为假命题,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/008d24253863cb430a7ca55f620faaa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50bce8d2d8368736b23470004f43f0c6.png)
(1)若p为真命题,求实数a的取值范围;
(2)若p或q为真命题,p且q为假命题,求实数a的取值范围.
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解题方法
10 . 若命题“
”是假命题,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1efa0fd4f70bea79ddb234aa1ab39df4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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