Let A and B be two sets. Prove that:

(A-B) union B=A if and only if B is a subset of A.

Consider,

A={1,2,3}

B={2,3}....(as B is subset of A)

Hence,

A - B = {1}

Also,by given condition,

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

  ={1,2,3}

  =A

Hence, it is proved...