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(本小题满分12分) 命题实数x满足(其中),命题实数满足 (Ⅰ)若,且为真,求...

(本小题满分12分) 命题6ec8aac122bd4f6e实数x满足6ec8aac122bd4f6e(其中6ec8aac122bd4f6e),命题6ec8aac122bd4f6e实数6ec8aac122bd4f6e满足6ec8aac122bd4f6e

(Ⅰ)若6ec8aac122bd4f6e,且6ec8aac122bd4f6e为真,求实数6ec8aac122bd4f6e的取值范围;

(Ⅱ)若6ec8aac122bd4f6e6ec8aac122bd4f6e6ec8aac122bd4f6e的充分不必要条件,求实数a的取值范围.

 

(Ⅰ). (Ⅱ). 【解析】本题考查复合命题的应用和必要条件、充分条件、充要条件的应用,是基础题.解题时要认真审题,仔细解答 (1)当a=1时,p真:1<x<3,q真:2<x≤4,由p∧q为真,能求出x的取值范围. (2)若¬p是¬q的充分不必要条件,则q是p的充分不必要条件,由a>0,知p:a<x<3a,q:2<x≤4,由此能求出a的取值范围. (Ⅰ)由得,又,所以, 当时,1<,即为真时实数的取值范围是1<.  ········· 2分 由得解得, 即为真时实数的取值范围是. ··················· 4分 若为真,则真且真,所以实数的取值范围是. ········· 6分 (Ⅱ)由(Ⅰ)知p:,则:或,··········· 8分 q:,则:或,···················· 10分 是的充分不必要条件,则,且, ∴解得,故实数a的取值范围是.··········· 12分
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