What are " " and " ". Do you mean A' and B', the complements of A and B?

To prove "set X = set Y" prove "set X is a subset of set Y" and then prove "set Y is a subset of set X"

To prove "set X is a subset of set Y" start by saying "if a is a member of X" and use whatever you know about X and Y to conclude "a is a member of Y".

To prove

(By the way is "\cup" and is "\cap".)

you need to prove that and then prove .

To prove the first: If then a is NOT in . That means that a is NOT in either A or B: and . From that it follows that and so