Let p(x), q(x), and r(x) denote the following open statements.
p(x): x2 - 8x + 15 = 0
q(x): x is odd
r(x): x > 0
For the universe of all integers, determine the truth or falsity of each of the following statements. If a statement is false, give a counterexample.
(a) ∀x [p(x) → q(x)]
(b) ∀x [q(x) → p(x)]
(c) ∃x [p(x) → q(x)]
(d) ∃x [q(x) → p(x)]
(e) ∃x [r(x) → p(x)]
(f) ∀x [¬q(x) → ¬p(x)]
(g) ∃x[p(x) → q(x) ∧ r(x))]
(g) ∀x[p(x) ∨ q(x)) → r(x))]