Question

With an example prove that A - (B U C) = (A - B) n (A - C) ​

Answer 1

As an example for which the equality holds, let A = {1, 2, 3}, B = {2}, and C = {3}. Then on the left side,

A - (B U C) = {1, 2, 3} - ({2} U {3})

… = {1, 2, 3} - {2, 3}

… = {1}

and on the right,

(A - B) ∩ (A - C) = ({1, 2, 3} - {2}) ∩ ({1, 2, 3} - {3})

… = {1, 3} ∩ {1, 2}

… = {1}