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

1个回答

  • U={x|x 2-3x+2≥0 }={x|(x-1)(x-2)≥0}={x|x≤1,或 x≥2},

    A={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

    x-2≠0 ={x|x≤1,或 x>2}.

    (1)A∩B={x|x<1,或x>3}∩{x|x≤1,或 x>2}={x|x<1,或 x>3}.

    (2)A∪B={x|x<1,或x>3}∪{x|x≤1,或 x>2}={x|x≤1,或 x>2}.

    (3)( C UA)∪( C UB)=C U (A∩B )={x|x=1,或 3≥x≥2}.

    (4)( C UA)∩( C UB)=C U ( A∪B )={x|x=2}={2}.