Question

Negation of the Boolean expression $p\iff (q\Rightarrow p)$ is

Answer 1

$p\iff (q\to p)$

$\sim (p\iff (q\iff p\left)\right)$

$\equiv \sim \left[\right(\sim p\vee (q\to p))\wedge (p\vee \sim (q\to p)\left)\right]$

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

$\equiv \sim [T\wedge (p\vee (q\wedge \sim p)\left)\right]$

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

$\equiv \sim \left[\right(p\vee q)\wedge T]$

$\equiv \sim p\wedge \sim q$