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Mathematical Reasoning
medium
The statement $( p \wedge q ) \Rightarrow( p \wedge r )$ is equivalent to.
A
$q \Rightarrow(p \wedge r)$
B
$p \Rightarrow( p \wedge r )$
C
$( p \wedge r ) \Rightarrow( p \wedge q )$
D
$(p \wedge q) \Rightarrow r$
(JEE MAIN-2022)
Solution
$( p \wedge q ) \Rightarrow( p \wedge r )$
$\sim( p \wedge q ) \vee( p \wedge r )$
$(\sim p \vee \sim q ) \vee( p \wedge r )$
$(\sim p \vee( p \wedge r )) \vee \sim q$
$(\sim p \vee p ) \wedge(\sim p \vee r ) \vee \sim q$
$(\sim p \vee r ) \vee \sim q$
$(\sim p \vee \sim q ) \vee r$
$\sim( p \wedge q ) \vee r$
$( p \wedge q ) \Rightarrow r$
Standard 11
Mathematics