Question

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

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

Answer 1

Answer: (C)

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