Prove the following equivalences without using truth tables, andspecify at each step of your proof the equivalence law you areusing.
(a) ¬ (p ∨ (¬ p ∧ q)) ≡ ¬ p ∧ ¬ q
(b) ( x → y) ∧ ( x → z) ≡ x → ( y ∧ z)
(c) (q → (p → r)) ≡ (p → (q → r))
(d) ( Q → P) ∧ ( ¬Q → P) ≡ P
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