Question: Let the universe for both variables x and y be the set {1, 2, 3, 4, 5, 6}. Let p(x, y) = x divides y.

Let the universe for both variables x and y be the set {1, 2, 3, 4, 5, 6}. Let p(x, y) = "x divides y." Give the truth values of each of the statements; explain your answer, and give a counterexample in the case that the statement is false.
(a) (x (y p(x, ( y)
(b) (x ∃y p(x, y)
(c) ∃x (y p(x, y)
(d) ∃y (x p(x, y)
(e) (y ∃x p(x, y)
(f) (x p(x, x)

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