Question

Which of the following option is incorrect?

• A. $\sim \left(p \Leftrightarrow \sim q\right)\equiv p\Leftrightarrow q$
• B. $\left(p \Leftrightarrow \sim q\right)\equiv \left(p \rightarrow \sim q\right)\land \left(\sim q \rightarrow p\right)$
• C. $\sim \left(p \Leftrightarrow q\right)\equiv \sim p\Rightarrow q$
• D. $\sim \left(p \Rightarrow q\right)\equiv p\land simq$

Answer 1

Answer: (C)

Option (D) is a theorem, hence (D) is correct
For option (B), $s\leftrightarrow t\equiv \left(s \rightarrow t\right)\land \left(t \rightarrow s\right)$ , hence (B) is correct
For option (A), $\sim \left(p \Leftrightarrow \sim q\right)\equiv p\Leftrightarrow \sim \left(\sim q\right)$
$\equiv p\Longleftrightarrow q$
Hence, (A) is correct
For option (C), $\sim \left(p \Leftrightarrow q\right)\equiv \sim p\Leftrightarrow q$
Hence, option (C) is incorrect