1. Tardigrade
  2. Question
  3. Mathematics
  4. Negation of the Boolean expression p Leftrightarrow(q ⇒ p) is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Negation of the Boolean expression
$p \Leftrightarrow(q \Rightarrow p)$ is

JEE MainJEE Main 2022Mathematical Reasoning

Solution:

$ \sim( p \leftrightarrow( q \rightarrow p ))$
$ \sim( p \leftrightarrow q )=( p \wedge \sim q ) \vee( q \wedge \sim p ) $
$ \sim( p \leftrightarrow( q \rightarrow p ))=( p \wedge \sim( q \rightarrow p )) \vee(( q \rightarrow p ) \wedge \sim p ) $
$( p \wedge \sim( q \rightarrow p ))= p \wedge( q \wedge \sim p )=( p \wedge \sim p ) \wedge q = c$
$( q \rightarrow p ) \wedge \sim p =(\sim q \vee p ) \wedge \sim p =\sim p \wedge(\sim q \vee p )$
$ (\sim p \wedge \sim q ) \vee(\sim p \wedge p )=\sim p \wedge \sim q $
$ \sim( p \leftrightarrow( q \rightarrow p ))= c \vee(\sim p \wedge \sim q )=\sim p \wedge \sim q $