Write the negation of each proposition in Exercises 1–4.
Exercise 1
Let P(x, y) be the propositional function x ≥ y. The domain of discourse is Z+ × Z+. Tell whether each proposition in is true or false.
∀x∀y P(x, y)
Exercise 2
Let P(x, y) be the propositional function x ≥ y. The domain of discourse is Z+ × Z+. Tell whether each proposition in is true or false.
ƎxƎy P(x, y)
Exercise 3
Let P(x, y) be the propositional function x ≥ y. The domain of discourse is Z+ × Z+. Tell whether each proposition in is true or false.
Ǝx∀y P(x, y)
Exercise 4
Let P(x, y) be the propositional function x ≥ y. The domain of discourse is Z+ × Z+. Tell whether each proposition in is true or false.
ƎxƎy P(x, y)
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