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) â€All people weigh at least 100 pounds.â€
(b) â€Somebody did not see any animals in the zooâ€
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.