Solutions

  1. Answer: a ⇔ e, d ⇔ f, g ⇔ h

  2. 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.

  3. 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.

  4. Answer: 0 → p and p → 1 are tautologies.