# The negation of the Boolean expression $\sim s\vee (\sim r\wedge s)$ is equivalent to : Option 1) $\sim s\wedge\sim r$ Option 2) r Option 3) $s\vee r$ Option 4) $s\wedge r$

negation of the Boolean expression $\sim s\vee (\sim r\wedge s)$ = $\sim(\sim s)\wedge\sim (\sim r\wedge s)$

Applying De morgans law,

$\sim(A\vee B)=\sim A \: \wedge \sim B$

$= s\wedge (\sim(\sim r)\vee (\sim s))$

=$(s\wedge r)\vee(s\wedge \sim s)$

Using double negation law and distributive law

$A\wedge (B\vee C)=(A\wedge B)\vee(A\wedge C)$

=> $(S\wedge r)\vee F$

Contradiction $(A\wedge \sim A)= F$

=> $(S\wedge r)$

So, option (4) is correct.

Option 1)

$\sim s\wedge\sim r$

Option 2)

r

Option 3)

$s\vee r$

Option 4)

$s\wedge r$

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