Problem 49E

In 47–50 (a) use the logical equivalences p →q ≡∼p ∨ q and p ↔ q ≡ (∼p ∨ q) ∧ (∼q ∨ p) to rewrite the given statement forms without using the symbol → or ↔, and (b) use the logical equivalence p ∨ q ≡∼(∼p∧ ∼q) to rewrite each statement form using only ∧ and ∼.

( p →r ) ↔ (q →r )

Solution:

Step 1:

In this problem, we have to rewrite the given statement

We have to use the logical equivalences p →q ≡∼p ∨ q and p ↔ q ≡ (∼p ∨ q) ∧ (∼q ∨ p) to rewrite the given statement forms without using the symbol → or ↔