Question

The negation of the statement $(p\to q)\wedge r$ is

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

Answer 1

The correct option is A $p\wedge \sim q\vee \sim r$

$p\to q$

$=\sim p\vee q---\left(1\right)$

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

$\sim [\sim p\vee q\wedge r]$...[form(i)]

$\sim (\sim p\vee q)\vee \sim r$...[Demorgans low]

$\sim (\sim p)\wedge \sim q\vee q\sim r$ $av(b\wedge c)$

$p\wedge \sim q\vee \sim r$ $=(a\vee b)\vee (a\vee c)]$