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The questions below consider the two propositions ∀x (P(x) ∨ Q(x)) and (∀x P(x)) ∨ (∀x Q(x))
where P and Q are predicates.
1) If P(x)=T, P(y)=F and Q(x)=F, Q(y)=T ; give a domain of discourse so that the two propositions are not equivalent.
2) If P(x)=F, P(y)=T and Q(x)=F, Q(y)=T ; give a domain of discourse so that they are equivalent.
3) What logical relationship holds between these two propositions? Explain.
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