Prove that A B A if and only if B ASolution1 Let A union BA

Prove that A B = A if and only if B A.

Solution

1. Let A union B=A

Let, x belong to B. Hence, x belong to A union B. But A union B=A

SO, x belongs to A

But x is arbitrary element in B so B is subset of A

2. Let, B subset A

Let x belong to A union B

So, x belong to A or B

But B subset A. So if x belongs to B then x belongs to A. So x belongs to A

Hence, A union B is subset of A

Let, x belong to A, so x belongs to A union B

Hence, A subset of A union B

Hence, A=A union B

Hence proved