Question

The statement $p\Rightarrow \left(q\wedge p\right)$ is negation of the statement

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

Answer 1

Answer: (C)

$\because \sim (s\Rightarrow t)\equiv s\wedge (\sim t)$
$\because \sim (p\Rightarrow (q\wedge p))\equiv p\wedge (\sim (q\wedge p))$
$\equiv p\wedge (\sim q\vee \sim p)$
$\equiv (p\wedge \sim q)\vee (p\wedge \sim p)$
$\equiv (p\wedge \sim p)\vee f$
$\equiv p\wedge \sim q\equiv \sim (p\Rightarrow q)$