(Solution) - Let p x q x and r x denote the following open statements p x -(2025 Original AI-Free Solution)

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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))]