2. In this problem, the domain of discourse is the set of positive integers: {1, 2,...
2. In this problem, the domain of discourse is the set of positive integers: {1, 2, 3, ...}. Which statements are true? If an existential statement is true, give an example. If a universal statement is false, give a counterexample.
(a) ∀x(x 2 − 1 > 0)
(b) ∀x(x 2 − x > 0)
(c) ∃x(x 3 = 8)
(d) ∃x(x + 1 = 0)
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2. In this problem, the domain of discourse is the set of
positive integers: {1, 2,...
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5. Suppose P(m,n) means “m>n”, where the universe of discourse for m and n is the set of POSITIVE integers. Find the truth value of each statement and explain your answer. NOTE: This is NOT exactly the same as the practice test. (a) (2 points) VxP(x,5) (b) (2 points) Vx3yP(x,y) (c) (2 points) ExWyP(x,y)
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