题干

设全集U=R,集合A={x|m﹣2<x<m+2,m∈R},集合B={x|﹣4<x<4}.

(Ⅰ)当m=3时,求A∩B,A∪B;

(Ⅱ)若A⊆∁UB,求实数m的取值范围.

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答案(点此获取答案解析)

【解答】解:(Ⅰ)当m=3时,A={x|1<x<5};

∴A∩B={x|1<x<4},A∪B={x|﹣4<x<5};

(Ⅱ)∁UB={x|x≤﹣4,或x≥4};

∵A⊆∁UB;

∴m﹣2≥4,或m+2≤﹣4;

∴m≥6,或m≤﹣6;

所以实数m的取值范围是(﹣∞,﹣6∪6,+∞).

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