若A={x∈Z|x^2-2x-3<=0},B={0,4,5}.全集U={x∈Z||x-1|<=4},求（CuA）∪B,A∩CuB及A的子集的个数
热心网友
若A={x∈Z|x^2-2x-3<=0},B={0,4,5}。全集U={x∈Z||x-1|<=4},求（CuA）∪B,A∩CuB及A的子集的个数 A:∵x^-2x-3≤0,∴-1≤x≤3∴A={-1,0,1,2,3}。U:|x-1|≤4∴-4≤x-1≤4∴-3≤x≤5∴U={-3,-2,-1,0,1,2,3,4,5}。CuA={-3,-2,4,5}。∴(CuA）∪B={-3,-2,4,5}∪{0,4,5}={-3,-2,0,4,5}CuB={-3,-2,-1,1,2,3}。∴A∩CuB={-1,0,1,2,3}∩{-3,-2,-1,1,2,3}={-1,1,2,3}∵A={-1,0,1,2,3}。A的子集的个数 2^5=32(个)Φ;{-1};{0};{1};{2};{3};{-1,0};{-1,1};{-1,2,};{-1,3};{0,1};{0,2,};{0,3};{1,2};{1,3};};{2,3};{-1,0,1};{-1,0,2};{-1,0,3};{-1,1,2};{-1,1,3};{-1,2,3};{0,1,2};{0,1,3};{0,2,3};{1,2,3};{-1,0,1,2,};{-1,0,1,3};{-1,0,2,3};{-1,1,2,3};{0,1,2,3};{-1,0,1,2,3};。
热心网友
A={-1,0,1,2,3},U={-3,-2,-1,0,1,2,3,4,5},CuA={-3,-2,4,5},CuA）∪B={-3,-2,0,4,5},A∩CuB={-1,12,3},A的子集的个数是2的五次方，即32个