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Question: Which of the following is always true...

Which of the following is always true

A

(p⇒q)≡ 6mu∼q⇒ 6mu∼p(p \Rightarrow q) \equiv \mspace{6mu}\sim q \Rightarrow \mspace{6mu}\sim p

B

∼(p∨q)≡∨ 6mup 6mu∨∼q\sim(p \vee q) \equiv \vee \mspace{6mu} p\mspace{6mu} \vee \sim q

C

∼(p⇒q)≡p 6mu∧∼q\sim(p \Rightarrow q) \equiv p\mspace{6mu} \land \sim q

D

∼(p∨q)≡ 6mu∼p 6mu 6mu∧∼q\sim(p \vee q) \equiv \mspace{6mu}\sim p\mspace{6mu}\mspace{6mu} \land \sim q

Answer

∼(p⇒q)≡p 6mu∧∼q\sim(p \Rightarrow q) \equiv p\mspace{6mu} \land \sim q

Explanation

Solution

p⇒q≡ 6mu∼p∨qp \Rightarrow q \equiv \mspace{6mu}\sim p \vee q ∴ ∼(p⇒q)≡p 6mu∧∼q\sim(p \Rightarrow q) \equiv p\mspace{6mu} \land \sim q.