Try It Now

Work these exercises to see how well you understand this material.

Answer: a ⇔ e, d ⇔ f, g ⇔ h
Solution: No. In symbolic form, the question is: Is (p → q) ⇔ (q → p)?

This table indicates that an implication is not always equivalent to its converse.
Solution: Let x be any proposition generated by p and q. The truth table for x has 4 rows and there are 2 choices for a truth value for x for each row, so there are 2 · 2 · 2 · 2 = 2⁴ possible propositions.
Answer: 0 → p and p → 1 are tautologies.