# Question: let px qx rx and sx y be propositional functions...

###### Question details

**Let P(x), Q(x), R(x), and S(x, y) be propositional
functions. For each proposition below, give a logically equivalent
proposition that uses only the universal quantifier ∀ and the
logical connectives ¬ and ∧.**

(a) ∃x (P(x) → Q(x))

(b) ∃x (¬Q(x) ↔ (P(x) ∧ R(x)))

(c) ∀x∃y ((S(x, y) ∧ Q(x)) → (R(x) ∨ R(y)))