The negation of $\sim \mathrm{s} \vee(\sim \mathrm{r} \wedge \mathrm{s})$ is equivalent to :

(C) $\mathrm{s} \wedge \mathrm{r}$

(A) $\mathrm{s} \wedge(\mathrm{r} \wedge \sim \mathrm{s})$

(B) $\mathrm{s} \vee(\mathrm{r} \vee \sim \mathrm{s})$

(D) $\mathrm{s} \wedge \sim \mathrm{r}$

JEE Main · 2015 · 04 Apr 2015 · Offline · Mathematical Reasoning *

The negation of

\sim s \lor (\sim r \land s)

is equivalent to :

Answer: (C)

Negate

\sim s \lor (\sim r \land s)

and push the negation inward. De Morgan turns it into

s \land \sim (\sim r \land s) = s \land (r \lor \sim s)

. Distributing,

s \land (r \lor \sim s) = (s \land r) \lor (s \land \sim s)

, and

s \land \sim s

is always false, so what survives is simply

s \land r

JEE Main · 2015 · 04 Apr 2015 · Offline · Single correct option