Consider the statement patterns A. (q p) (p q) B. ( p q) (p q) C. [(p q) p] q D. (p q) ( p q) then statement patterns

Step-by-step solution

For statement pattern A: (q p) (p q) ( q p) ( p q) ( q q) ( p p) T T T Thus, A is a tautology. For statement pattern B: By De Morgan's Law, (p q) p q . The statement becomes ( p q) ( p q) , which is of the form X X T . Thus, B is a tautology. For statement pattern C: [(p q) p] q [(p p) (q p)] q [F (q p)] q (q p) q p (q q) p F F Thus, C is a contradiction. For statement pattern D: (p q) ( p q) (p q) (p q) , which is of the form X X F . Thus, D is a contradiction. Therefore, A and B are tautologies, while C and D are