problem 10 : Explain why ∃xP(x) ∨ ∃xQ(x) ≡ ∃x(P(x) ∨ Q(x)). You need not formally...

problem 10 :

Explain why ∃xP(x) ∨ ∃xQ(x) ≡ ∃x(P(x) ∨ Q(x)). You need not formally prove it, but you should give a convincing explanation for why it is true?

Use the fact established in the problem that ∃xP(x) ∨ ∃xQ(x) ≡ ∃x(P(x) ∨ Q(x)) to prove that ∀xP(x) ∧ ∀xQ(x) ≡ ∀x(P(x) ∧ Q(x)).
Use Problem 10 above to prove that ∀xP(x) → ∃xP(x) ≡ T

Expert Solution

Colby Messinger answered 2 years ago

give an example to show it is false or argue why it is true. ∃!xP(x)⇒∃xP(x) ∃xP(x)⇒∃!xP(x)...

give an example to show it is false or argue why it is true. ∃!xP(x)⇒∃xP(x) ∃xP(x)⇒∃!xP(x) ∃!x¬P(x)⇒¬∀xP(x)

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