Question

Which of the following option is incorrect?

• A. $\sim \left(p\iff \sim q\right)\equiv p\iff q$
• B. $\left(p\iff \sim q\right)\equiv \left(p\to \sim q\right)\wedge \left(\sim q\to p\right)$
• C. $\sim \left(p\iff q\right)\equiv \sim p\Rightarrow q$
• D. $\sim \left(p\Rightarrow q\right)\equiv p\wedge simq$

Answer 1

Answer: (C)

Option (D) is a theorem, hence (D) is correct
For option (B), $s\leftrightarrow t\equiv \left(s\to t\right)\wedge \left(t\to s\right)$ , hence (B) is correct
For option (A), $\sim \left(p\iff \sim q\right)\equiv p\iff \sim \left(\sim q\right)$
$\equiv p⟺q$
Hence, (A) is correct
For option (C), $\sim \left(p\iff q\right)\equiv \sim p\iff q$
Hence, option (C) is incorrect