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  4. Negation of the Boolean statement ( p ∨ q ) ⇒((∼ r ) ∨ p ) is equivalent to:

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Q. Negation of the Boolean statement $( p \vee q ) \Rightarrow((\sim r ) \vee p )$ is equivalent to:

JEE MainJEE Main 2022Mathematical Reasoning

Solution:

$ P \vee q \Rightarrow(\sim r \vee p )$
$\equiv \sim( p \vee q ) \vee(\sim r \vee p ) $
$\equiv(\sim p \wedge \sim q ) \vee( p \vee \sim r )$
$\equiv[\sim p \vee p ) \wedge(\sim q \vee p )] \vee \sim r$
$\equiv[\sim q \vee p ) \vee \sim r$
Its negation is $\sim p \wedge q \wedge r$