Question

Negation of the statement $(p\wedge r)\to (r\vee q)$ is equivalent to

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

Answer 1

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

$(p\wedge r)\to (r\vee q)$
Using conditional Dejunction
$\sim (\sim (p\wedge r)\vee (r\vee q\left)\right)$
Using Demorgan's Law
$\sim \sim (p\wedge r)\wedge \sim (r\vee q)$
Double Negation
$(p\wedge r)\wedge \sim (r\vee q)$
It is further reduced to
$(p\wedge r)\wedge (\sim r\wedge \sim q)$
Option A.