Rules of Replacement III

Question 1

Law of Material Implication

Answer 1

(p -> q) <=> (~p v q)

Question 2

Laws of Material Equivalence

Answer 2

(p <-> q) <=> (p -> q) ^ (q -> p)
(p <-> q) <=> (p ^ q) v (~p ^ ~q)

Question 3

Law of Contraposition

Answer 3

(p -> q) <=> (~q -> ~p)

Question 4

Law of Exportation

Answer 4

((p ^ q) -> r) <=> (p -> (q -> r))

Question 5

Negation of an Implication

Answer 5

~(p -> q) <=> (p ^ ~q)