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数学
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已知命题p:x
2
+2x-3>0;命题q:x>a,且¬q的一个充分不必要条件是¬p,则a的取值范围是( )
A. a≥1
B. a≤1
C. a≥-1
D. a≤-3
人气:352 ℃ 时间:2020-01-09 06:36:31
解答
由x
2
+2x-3>0得x>1或x<-3,
即p:x>1或x<-3,¬p:-3≤x≤1,
∵q:x>a,∴¬q:x≤a,
若¬q的一个充分不必要条件是¬p,
则¬p⇒¬q成立,但¬q⇒¬p不成立,
∴a≥1,
故选:A.
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