题目内容
(本小题满分12分)
已知命题
:实数
满足
;命题
:实数
满足
,若
是
的必要不充分条件,求实数
的取值范围.
已知命题
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447377279.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447393249.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447424595.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447440293.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447393249.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447487868.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447502293.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447533316.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447549298.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232344475801223.png)
本试题主要是考查了命题的真值以及充分条件和必要条件的判定的运用
先根据已知条件,得到![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232344475961562.png)
然后因为“若
则
”的逆否命题为 “若
则
”,又
是
的必要不充分条件,∴
是
的必要不充分条件,可知集合的包含关系得到结论。
解:令![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232344478141564.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232344476272358.png)
∵ “若
则
”的逆否命题为 “若
则
”,又
是
的必要不充分条件,∴
是
的必要不充分条件,
∴AÞ B ,故![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232344475801223.png)
先根据已知条件,得到
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232344475961562.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232344476272358.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447643325.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447658329.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447689310.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447705313.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447643325.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447658329.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447689310.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447705313.png)
解:令
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232344478141564.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232344476272358.png)
∵ “若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447643325.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447658329.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447689310.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447705313.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447643325.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447658329.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447689310.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234447705313.png)
∴AÞ B ,故
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232344475801223.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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