Can I receive help with the questions?

Show that p E |p>(r A ;r) with a truth table. Why does this illustrate the validity of a proof by contradiction? Use a direct proof to show that the sum of two odd integers is even. Prove that the product of two rational numbers is rational. Prove the following theorem: \"if A and B are sets, then ?(A n B) E 33(A) n ?(B).\