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Mathematical Reasoning
medium
The negation of the statement $(p \vee q)^{\wedge}(q \vee(\sim r))$ is
A
$((\sim p) \vee r) \wedge(\sim q)$
B
$((\sim p) \vee(\sim q))^{\wedge}(\sim r)$
C
$((\sim p) \vee(\sim q)) \vee(\sim r)$
D
$(p \vee r)^{\wedge}(\sim q)$
(JEE MAIN-2023)
Solution
$\sim[(p \vee q) \wedge(q \vee(\sim p)]$
$\Rightarrow \sim(p \wedge q) \vee \sim(q \vee(\sim p))$
$\Rightarrow(\sim p \wedge \sim q) \vee(\sim q \wedge p)$
Apply distribution law
$\Rightarrow \sim q \wedge(\sim p \vee p )$
$\Rightarrow(\sim p \vee p ) \wedge(\sim q )$
Standard 11
Mathematics
