p q ~p ~q ~p ∨ ~q ~(~p ∨ ~q)
T T F F F T
T F F T T F
F T T F T F
F F T T T F
You start by listing TTFF under p, and then TFTF under q. Then apply the rules of negation, conjunction, disjuction, and implication as is appropriate to fill in the rest. For example, in the first row, p is true, so not p is false, and q is true, so not q is false. Disjunction says that false or false is false so not p (false) or not q (false) is false. And the last column is just not false is true.
John

My calculator said it, I believe it, that settles it