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Mathematical Reasoning
hard
मिश्र कथन $(\sim(\mathrm{P} \wedge \mathrm{Q})) \vee((\sim \mathrm{P}) \wedge \mathrm{Q}) \Rightarrow((\sim \mathrm{P}) \wedge(\sim \mathrm{Q}))$ किस के तुल्य है ?
A
$((\sim P ) \vee Q ) \wedge((\sim Q ) \vee P )$
B
$(\sim Q) \vee P$
C
$((\sim P ) \vee Q ) \wedge(\sim Q )$
D
$(\sim P ) \vee Q$
(JEE MAIN-2023)
Solution
Let $\quad r =(\sim( P \wedge Q )) \vee((\sim P ) \wedge Q ) ; \quad s =$ $((\sim P ) \wedge(\sim Q ))$
Option (A) : $((\sim P ) \vee Q ) \wedge((\sim Q ) \vee P )$ is equivalent to (not of only $P) \wedge($ not of only $Q$) $=($ Both $P , Q )$ and (neither $P$ nor $Q )$
Standard 11
Mathematics
