Consider the following:F → (B ∨ A)D → F¬(B ∨ A)..∴ ¬(D ∧ C)Which of the following can be derived from the premises?¬B ∨ ¬A¬(D ∨ C)¬B ∧ ¬A¬D

Show that the following formulas are tautologies:(a) ¬(A ^ B) , ¬A _ ¬B(b) A ) B , ¬B ) ¬A(c) ((A ) B) ^ (B ) A)) , (A , B)(d) (A _ B) ^ (¬B _ C) ) (A _ C)

. If A is true and B is true, what is the value of ¬A ∨ B?*4 points¬A ∨ B is True¬A ∨ B is False

_ _ _ _ _ _ _ _ _ _ _    TC13: 9*∀z (h(z) ∧ s(z)) → ∃z m(z)h(y) → m(y)∀x(h(x) → m(x))h(y) ∧ s(y) → m(y)¬h(y) ∨ m(y)¬(h(y) ∧ s(y)) ∨ m(y)

Using Boolean laws simplify each of the following propositions:a. a ∧ b ∨ a ∧ ¬b

Show that ¬(𝑝 ∨ (¬𝑝 ∧ 𝑞)) and ¬𝑝 ∧ ¬𝑞 are logically equivalent by:a) Using a truth table (3 POINTS)b) Using logical equivalences