Question

The negation of $\sim s\vee (\sim r\wedge s)$ is equivalent to

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

Answer 1

The correct option is D $s\wedge r$

$\sim (\sim s\vee (\sim r\wedge s\left)\right)\equiv \sim (\sim s)\wedge \sim (\sim r\wedge s)\equiv s\wedge (\sim (\sim r)\vee \sim s)\equiv s\wedge (r\vee \sim s)\equiv (s\wedge r)\vee (s\wedge \sim s)\equiv (s\wedge r)\vee F[\because s\wedge \sim sisfalse]\equiv s\wedge r$