Question

一道集合题

已知全集U={x|x≤1或x≥2} A={x<1或x>3} B={x≤1或x>2}，求CuA,CuB,A∩B,A∩(CuB),(CuA)∩B

Answer 1

U={x|x≤1 or x≥2}, A={x|x<1 or x>3}, B={x|x≤1 or x>2}，

CuA = U-A
= {x|x≤1 or x≥2} - {x|x<1 or x>3}
= {x| x=1 or 2≤x≤3}
CuB = U-B
= {x|x≤1 or x≥2}- {x|x≤1 or x>2}
= {2}
A∩B = {x|x<1 or x>3}∩{x|x≤1 or x>2}
= {x|x<1 or x>3}
A∩(CuB)= {x|x<1 or x>3}∩{2}
= ø
(CuA)∩B = {x| x=1 or 2≤x≤3} ∩ {x|x≤1 or x>2}
= {x| x=1 or 2<x≤3}