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Mathematical Reasoning
hard
The proposition $ \sim \left( {p\,\vee \sim q} \right) \vee \sim \left( {p\, \vee q} \right)$ is logically equivalent to
A
$p$
B
$q$
C
$\sim p$
D
$\sim q$
(JEE MAIN-2014)
Solution
Given $ \sim \left( {p \vee \sim q} \right) \vee \sim \left( {p \vee q} \right)$
$ \equiv \left( { \sim p \vee q} \right) \vee \sim \left( {p \vee \sim q} \right)$
$ \equiv \sim p \vee \left( {q \vee \sim p} \right)$
$ \equiv \sim p$
Standard 11
Mathematics
