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Mathematical Reasoning
hard
कथन $(P \Rightarrow Q) \wedge(R \Rightarrow Q)$ किसके तार्किक तुल्य है
A
$( P \vee R ) \Rightarrow Q$
B
$( P \Rightarrow R ) \wedge( Q \Rightarrow R )$
C
$( P \Rightarrow R ) \vee( Q \Rightarrow R )$
D
$(P \wedge R) \Rightarrow Q$
(JEE MAIN-2023)
Solution
$( P \Rightarrow Q ) \wedge( R \Rightarrow Q )$
We known that $P \Rightarrow Q \equiv \sim P \vee Q$
$\Rightarrow(\sim P \vee Q ) \wedge(\sim R \vee Q )$
$\Rightarrow(\sim P \wedge \sim R ) \vee Q$
$\Rightarrow \sim( P \vee R ) \vee Q$
$\Rightarrow( P \vee R ) \Rightarrow Q$
Standard 11
Mathematics
