3. Consider p(x) and g(x), where x U = {1,2}. If the following is true, give a rigorous argument. If it is false, give a counterexample. (Note that "p implies q" is the same as "if p, then q" and also as "pq.") (i) (Vx = U, p(x) q(x)) implies [ (Vx U, p(x)) (Vx U, q(x)) ] ? What about its converse ? (ii) (3x = U, p(x) q(x)) implies [ (3x U, p(x)) (3x U, q(x)) ] ? What about its converse ?