Question

Suppose a conditional statement and its converse are both true. What are the truth values of the contrapositive and inverse? How do you know?

Answer 1

Rule1: Any conditional statement is going to have the same truth value as it's contrapositive

Rule2: Any converse (of some conditional statement) is going to have the same truth value as the inverse (of that same original statement)

Answer 2

Original Statement: P --> Q (read this as "if P, then Q")

Converse: Q --> P

Inverse: ~P --> ~Q (this is "if not P, then not Q")

Contrapositive: ~Q --> ~P

Answer 3

^ ah man, logic was fun.