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

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