QJEEM22Ma0a9b: JEE Main 2022 Mathematics - Class 11 JEEM22Ma0a9b Solution: Negation of the Boolean statement (p ∨ q) ⇒ (( ∼ r) ∨ p) is…

Question

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

Accepted Answer

Given,

(p $\lor$ q) $\Rightarrow$ (( $\sim$ r) $\lor$ p)

Negation is

$\sim$ ((p $\lor$ q) $\Rightarrow$ ( $\sim$ r) $\lor$ p))

= (p $\lor$ q) $\land$ $\sim$ (( $\sim$ r) $\lor$ p)

= (p $\lor$ q) $\land$ (r $\land$ $\sim$ p)

[(p $\land$ $\sim$ p) $\lor$ (q $\land$ $\sim$ p)] $\land$ r

= q $\land$ $\sim$ p $\land$ r

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