Question

The proposition $\sim (p\iff q)$ is equivalent to

• A. $(p\vee \sim q)\wedge (q\wedge \sim p)$
• B. $(p\wedge \sim q)\vee (q\wedge \sim p)$
• C. $(p\wedge \sim q)\wedge (q\wedge \sim p)$
• D. None of the above

Answer 1

The correct option is B $(p\wedge \sim q)\vee (q\wedge \sim p)$

$\sim (p\iff q)\equiv \sim \left[\right(p\Rightarrow q)\wedge (q\Rightarrow p\left)\right]$

$\equiv \sim (p\Rightarrow q)\vee (\sim (q\Rightarrow p\left)\right)$ .......

($\because$ De-Morgan's law)

$\equiv (p\wedge \sim q)\vee (q\wedge \sim p)$

Hence, option B is correct.