Question

已知全集U=｛x|x²-3x+2≥0｝，A=｛x|x²-4x+3＞0｝，B=｛x|(x-1)÷(x-2)≥0｝

求A∩B，
A∪B，
(CuA)∪(CuB)，
(CuA)∩(CuB)，
详细易懂的过程。谢谢。、

Answer 1

U=｛x|x²-3x+2≥0｝=｛x|(x-1)(x-2)≥0｝=｛x|x<=1或x≥2｝，
A=｛x|x²-4x+3＞0｝=｛x|(x-1)(x-3)>0｝=｛x|x<1或x>3｝，
B=｛x|(x-1)÷(x-2)≥0｝=｛x|(x-1)(x-2)>=0且x不等于2｝=｛x|x<=1或x>2｝，
A∩B=｛x|x<1或x>3｝∩｛x|x<=1或x>2｝=｛x|x<1或x>3｝=A
A∪B=｛x|x<1或x>3｝∪｛x|x<=1或x>2｝=｛x|x<=1或x>2｝=B
CuA=U\A=｛x|x<=1或x≥2｝\｛x|x<1或x>3｝=｛x|x=1或2<=x<=3｝，
CuB=U\B=｛x|x<=1或x≥2｝\｛x|x<=1或x>2｝=｛x|x=2｝，
(CuA)∪(CuB)=｛x|x=1或2<=x<=3｝∪｛x|x=2｝=｛x|x=1或2<=x<=3｝，
(CuA)∩(CuB)=｛x|x=1或2<=x<=3｝∩｛x|x=2｝=｛x|x=2｝

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