SOLVED: Exercise 1.8.4: Using De Morgan's law for quantified statements to prove logical equivalenceUse De Morgan's law for quantified statements and the laws of propositional logic to show the following equivalences:(a) -∀x (P(x) ∨ Q(x)) = ∃x (-P(x) ∧ Q(x))(b) (∀xO(x) ∨ ∀xd(x)) ∧ ∃E = (∀xO(x) ∧ ∀xd(x)) ∧ ∀A(c) -∃x (-P(x) ∨ (Q(x) ∧ -R(x))) = ∨x (P(x) ∧ (-Q(x) ∨ R(x)))
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