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Mathematical Reasoning
hard
For any two statements $p$ and $q,$ the negation of the expression $p \vee ( \sim p\, \wedge \,q)$ is
A
$p \leftrightarrow q$
B
$\sim p\, \vee \,\sim q$
C
$\sim p\, \wedge \,\sim q$
D
$p\, \wedge \,q$
(JEE MAIN-2019)
Solution
$ \sim \left( {p \vee \left( { \sim p \wedge q} \right)} \right)$
$ = \sim p \wedge \sim \left( { \sim p \wedge q} \right)$
$ = \sim p \wedge \left( {p \vee \sim q} \right)$
$ = \left( { \sim p \wedge p} \right) \vee \left( { \sim p \wedge \sim q} \right)$
$ = c \vee \left( { \sim p \wedge \sim q} \right)$
$ = \left( { \sim p \wedge \sim q} \right)$
Standard 11
Mathematics
