Question

If A,B and C are any three sets, then prove that : =(AUB)-C=
(A-C)U(B-C)

Answer 1

Answer:

let A={1,2,3,4,5,6} B={3,4,5,9} and C={7,8,9}

(AUB)-C=({1,2,3,4,5,6}U{3,4,5,9})-{7,8,9}

{1,2,3,4,5,6,9}-{7,8,9}÷{1,2,3,4,5,6}

again (A-C)-(B-A)=({1,2,3,4,5,6}-{7,8,9})-({3,4,5,9}-{1,2,3,4,5,6}

then {1,2,3,4,5,6}-{9}={1,2,3,4,5,6}

hence (AUB)-C=(A-C)-(B-A)