THE PROPOSITION CAN BE FALSE

SOLUTION MANUAL FOR DISCRETE MATHEMATICS 7TH EDITION BY JOHNSONBAUGH

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75. The proposition can be false. Let P(x, y) be the statement x > y and let the domain of discourse

be Z

⁺

× Z

⁺

. Then ∃x∃yP (x, y) is true, but ∀x∃yP (x, y) is false.