Question

设集合A={x|x²-1＞0},B={x|log₂x＞0},则A∩B等于(    )

A.{x|x＞1}         B.{x|x＞0}             C.{x|x＜-1}              D.{x|x＜-1或x＞1}

Answer 1

A

解法一:∵x²＞1,∴x＞1或x＜-1.∴A={x|x＞1或x＜-1}.

又log₂x＞0,即log₂x＞log₂1,∴x＞1.∴B={x|x＞1}.∴A∩B={x|x＞1}.

解法二:(排除法)B、C、D不满足log₂x＞0,故选A.