Am I understanding proof by contradiction correctly? In order to prove a conditional p->q, we need to assume p /\ ~q to be true and show that a contradiction follows. The idea is that (p /\ ~q) -> F = T means the (p /\ ~q) is false correct? Then from p /\ ~q being false, it means that ~(p/\~q) is true. By De Morgans, ~p \/ q is true and since p -> q = ~p \/ q, we have shown that p -> q is true.