Question

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

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

Answer 1

Answer: (A), (C)

The correct options are
A $s\wedge (r\vee \sim s)$
C $s\wedge r$

We have to find $\sim [\sim s\vee (\sim r\vee s\left)\right]$
We use set theory approach.
$[S^c\cup (R^c\cap S){]}^c$
$=S\cap (R\cup S^c)$
This can be represented as $s\wedge (r\vee \sim s)$.

$[S^c\cup (R^c\cap S){]}^c$
$=\left[\right(S^c\cup R^c)\cap (S^c\cup S){]}^c$
$=\left[\right(S^c\cup R^c)\cup U{]}^c$
$=\left[\right(S^c\cup R^c){]}^c$
$=S\cap R$
This can be represented as $s\wedge r$.