1. Tardigrade
  2. Question
  3. Mathematics
  4. The statement (p ∧ q) ⇒(p ∧ r) is equivalent to :

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The statement $(p \wedge q) \Rightarrow(p \wedge r)$ is equivalent to :

JEE MainJEE Main 2022Mathematical Reasoning

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 $