Question 4: Prove that the following proposition is a tautology (using the rules of inference below).

((p q) q) p

Question 5: Prove that the following proposition is a tautology (using the rules of inference below).

p q (p q)

Modus ponens Modus tollens: introduction: elimination [or ] V eliinalion: Case analysis) _' Introduction: a elimination: tintroduction: ++ elimination: at ( ) ( ) Contradiction: Tautology (when a TRUE) FALSE Figure 3.1: Rules of Inference