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) xy ((S(x, y) Q(x)) (R(x) R(y)))