Question

if U=(1,2,3,4,5,6,7,8,9) A=(2,4,6,8) B=(2,3,5,7) verify that (A-B)U(B-A)=(AUB)- (AB)​

Answer 1

Answer.

A=(2,4,6,8),. B=(2,3,5,7)

We have to prove

(A-B)U(B-A)=(AUB)-(AnB)

Lhs

A-B={2,4,6,8}-{2,3,5,7}

={4,6,8}

B-A={2,3,5,7}-{2,4,6,8}

={3,5,7}

(A-B)U(B-A)={3,4,5,6,7,8}

RHS.

AUB={2,4,6,8}U{2,3,5,7}

={2,3,4,5,6,7,8}

AnB={2,4,6,8}n{2,3,5,7}

={2}

(AUB)-(AnB)={3,4,5,6,7,8}

LHS=RHS. ( Proved)