Question

已知集合u=R,A={x|x^2-2x-3<0},B={x|1-x/x+2≤0},求A∩B,A∪B，(CuA)∩(CuB),Cu(A∩B)

Answer 1

A=｛x｜-1<x<3｝

B=｛x｜x≥1或x<-2｝

A∩B=｛x｜1≤x＜3｝

A∪B=｛x｜x>-1或x<-2｝

(CuA)∩(CuB)=｛x｜x≥3或，x≤-1｝∩｛x｜-2≤x<1}={x|-2≤x≤-1}

Cu(A∩B)={x|x<1或x≥3｝

Answer 2

A={x|x^2-2x-3<0},
={x| (x-3)(x+1)<0 }
={x| -1<x<3 }

B={x|(1-x)/(x+2) ≤0 }
={x| x ≥ 1 or x< -2 }

A∩B = {x| -1<x<3 } ∩{x| x ≥ 1 or x< -2 }
={x| 1≤x<3 }

A∪B = {x| -1<x<3 }∪ {x| x ≥ 1 or x< -2 }
={x| x<-2 or x>-1 } #

(CuA)∩(CuB) = Cu(A∪B)
= {x | -2≤x≤-1 } #

Cu(A∩B)= Cu( {x| 1≤x<3 } )
={x| x<1 or x≥ 3 } #