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Mathematical Reasoning
hard
माना $p$ तथा $q$ दो कथन है। तब $\sim(\mathrm{p} \wedge(\mathrm{p} \Rightarrow \sim \mathrm{q}))$ किस के समतुल्य है
A
$p \vee( p \wedge(\sim q ))$
B
$p \vee((\sim p ) \wedge q )$
C
$(\sim p ) \vee q$
D
$p \vee( p \wedge q )$
(JEE MAIN-2023)
Solution
$\sim( p \wedge( p \rightarrow \sim q ))$
$\equiv \sim p \vee \sim(\sim p \vee \sim q )$
$\equiv \sim p \vee( p \wedge q )$
$\equiv(\sim p \vee p ) \wedge(\sim p \vee q )$
$\equiv t \wedge(\sim p \vee q )$
$\equiv \sim p \vee q$
Standard 11
Mathematics
