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Mathematical Reasoning
hard
The negation of the Boolean expression $ \sim \,s\, \vee \,\left( { \sim \,r\, \wedge \,s} \right)$ is equivalent to
A
$s\, \vee r$
B
$ \sim \,s\, \wedge \, \sim \,r$
C
$r$
D
$s\, \wedge r$
(JEE MAIN-2019)
Solution
$ \sim \left( { \sim s \vee \left( { \sim \wedge s} \right)} \right)$
$s \wedge \left( {r \vee \sim s} \right)$
$\left( {s \wedge r} \right) \vee \left( {s \wedge \sim s} \right)$
$\left( {s \wedge r} \right) \vee \left( \phi \right)$
$\left( {s \wedge r} \right)$
Standard 11
Mathematics
