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))]
h) ∀x[p(x)˅ q(x)) r(x)]
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