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

The correct option is C $(p\wedge q)\wedge (p\wedge \sim r)$

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