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In: Advanced Math

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

1. Identify each of the following statements as true of false and explain your reasoning in full sentences. The domain of discourse 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. Your negation 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 true that∀x(P(x)∨ Q(x)), must ∀xP(x)∨∀xQ(x) also be true? Explain.

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Colby Messinger answered 1 year ago
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