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Mathematical Reasoning
hard
The negation of the expression $q \vee((\sim q) \wedge p)$ is equivalent to
A
$(\sim p ) \wedge(\sim q)$
B
$p \wedge(\sim q )$
C
$(\sim p ) \vee(\sim q)$
D
$(\sim p ) \vee q$
(JEE MAIN-2023)
Solution
$\sim(q \vee((\sim q) \wedge p))$
$= \sim q \wedge \sim((\sim q) \wedge p)$
$= \sim q \wedge(q \vee \sim p)$
$= (\sim q \wedge q) \vee(\sim q \wedge \sim p)$
$= (\sim q \wedge \sim p)$
Standard 11
Mathematics
