Show that the set {→, 1} is an adequate set for propositional logic 2. by expressing ¬0, ¢ V ý, and OA in terms of →, 1, ø, and .

Which of the following is a logical equivalence in first-order logic? A. ¬(∀x)P(x) ≡ (∃x)¬P(x) B. (∀x)(∃y)P(x, y) ≡ (∃y)(∀x)P(x, y) C. (∀x)(P(x) → Q(x)) ≡ (∃x)(P(x) ∧ Q(x)) D. (∀x)(P(x) ∧ Q(x)) ≡ (∀x)(P(x) ∨ Q(x))

2. Using logical equivalence, prove that (p^q)⇒(q⇒p) is a tautology. In other words, show that (pa)(a⇒p)=T You have to give clear reasons for each step!

JUST ANSWER A) AND D)