T or F:

Suppose that A and B are bounded sets in the real numbers.

1) sup (A U B) = max {sup A, sup B}

2) If the elements of A and B are positive and A.B = {ab | a is in A, b is in B}, then sup(A.B) = sup(A)sup(B)

3) The analogous problems for the greatest lower bound.

I believe all of them are true, but just wanted to make sure before I started on the proofs. Thanks!