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Mathematical Reasoning
medium
The Boolean expression $\sim\left( {p\; \vee q} \right) \vee \left( {\sim p \wedge q} \right)$ is equivalent ot :
A
$p$
B
$q$
C
$\sim q$
D
$\sim p$
(JEE MAIN-2018)
Solution
$ \sim \left( {p \vee q} \right) \vee \left( { \sim p \wedge q} \right)$
$\left( { \sim p \wedge \sim q} \right) \vee \left( { \sim p \wedge q} \right) \Rightarrow \sim p \wedge \left( { \sim p \vee q} \right)$
$ \Rightarrow \sim p \wedge t \equiv \sim p$
Standard 11
Mathematics
