Answer to Question #227726 in Discrete Mathematics for Varshi

Question

3) Using basic propositional equivalence (which we did in the class) show that (pr) ^ (4)

and (pvg) → are logically equivalent. (Don't use truth table for this problem)

O

U

Answer 1

$\neg(p \land \neg q) \lor r\\ \equiv [(\neg p) \lor (\neg( \neg q))] \lor r\\ \equiv [(\neg p) \lor q] \lor r\\ \equiv (\neg p) \lor (q \lor r)\\ \equiv p \to (q \lor r)\\ \equiv (p \lor q) → r$