Please show work if needed.

For each of the following, determine whether it is valid or invalid. If valid then give a proof. If invalid then give a counter example. A C and B C A union B C (B C) C A (C - A) interset (B - A) = (A B) - {A n B) = A B = (A times C) union (B times D) = (A union B) times (C union D). For each of the following, determine whether it is valid or invalid. If valid then give a proof. If invalid then give a counter example. A C and B C A union B C (B C) C A (C - A) interset (B - A) = (A B) - {A n B) = A B = (A times C) union (B times D) = (A union B) times (C union D)