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  3. 1. identify each of the following statements as tr

1. Identify each of the following statements as true of false and explain your reasoning in...

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Advance Math

1. Identify each of the following statements as true of falseand explain your reasoning in full sentences. The domain ofdiscourse is the integers.

(a) ∃x∀y(y > x)

(b) ∀y∃x(y > x)

(c) ∃x(x = 0 → x = 1)

2. Write the formal negation of the following statements. Yournegation must not contain any explicit negation symbols.

(a) ∀x∃y(2 < x ≤ y)

(b) ∀y∃x(y > 0 → x ≤ 0)

3. Negate verbally:
(a) ”All people weigh at least 100 pounds.”

(b) ”Somebody did not see any animals in the zoo”

4. If P and Q are predicates over some domain, and if it is truethat∀x(P(x)∨ Q(x)), must ∀xP(x)∨∀xQ(x) also be true? Explain.

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