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

The negation of $\sim s \vee(\sim r \vee s)$ is equivalent to
  1. $s \wedge r$
  2. $\sim r \wedge s$
  3. $s \wedge(r \wedge \sim s)$
  4. $s \wedge(r \vee \sim s)$

Solution

$\begin{aligned} & \sim\{\sim s \vee(\sim r \wedge s)\} \equiv \sim(\sim s) \wedge\{\sim(\sim r \wedge s)\} \\ & \equiv s \wedge\{\sim(\sim r) \vee \sim s\} \\ & \equiv s \wedge\{r \vee \sim s\} \\ & \equiv(s \wedge r) \vee(s \wedge \sim s) \\ & \equiv(s \wedge r) \vee c \\ & \equiv(s \wedge r)\end{aligned}$

Asked in: MHT CET 2022 (08 Aug Shift 2)

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