Question

Which of the following is true

• A. $p \Rightarrow q \equiv \mspace{6mu}\sim p \Rightarrow \mspace{6mu}\sim q$
• B. $\sim(p \Rightarrow \mspace{6mu}\sim q) \equiv \mspace{6mu}\sim p \land q$
• C. $\sim(\sim p \Rightarrow \sim q) \equiv \sim p \land q$
• D. $\sim(p \Leftrightarrow q) \equiv \lbrack\sim(p \Rightarrow q) \land \sim(q \Rightarrow p)\rbrack$

Answer 1

Answer: (C)

$\sim(\sim p \Rightarrow \sim q) \equiv \sim p \land q$

Answer 2

$\sim(p \Rightarrow q) \equiv p\mspace{6mu} \land \sim q$

∴ $\sim(\sim p \Rightarrow \mspace{6mu}\sim q) \equiv \mspace{6mu}\sim p\mspace{6mu} \land \sim(\sim q) \equiv \mspace{6mu}\sim p \land q$

Thus $\sim(\sim p \Rightarrow \mspace{6mu}\sim q) \equiv \mspace{6mu}\sim p \land q$.