The logical statement& [∼ (∼ p ∨ ∼ q) ∨ (p ∧ r)] ∧ (q ∧ r) is equivalent to

Correct answer: D. (p ∧ r) ∧ q (( ( p q) (p r)) ( q r)) (=((p q) (p r)) ( q r)) (=(p ( q r)) ( q r)) (=p ( q r)=p ( q) r)

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Mathematical Reasoning

NTA Abhyas 2020 · Mathematics · Mathematical Reasoning

The logical statement& [∼ (∼ p ∨ ∼ q) ∨ (p ∧ r)] ∧ (q ∧ r) is...

The logical statement&

\left[∼ \left(∼ p ∨ ∼ q\right) ∨ \left(p ∧ r\right)\right] ∧ \left(q ∧ r\right)

is equivalent to$$

Options

A $\left(p ∧ q\right) ∨ r$
B $∼ p ∨ r$
C $\left(∼ p ∧ q\right) ∧ r$
D $\left(p ∧ r\right) ∧ q$

Correct answer

D. $\left(p ∧ r\right) ∧ q$

Step-by-step solution

((\sim(\sim p \vee q) \vee(p \wedge r)) \wedge(\sim q \wedge r)) (=((p \wedge \sim q) \vee(p \wedge r)) \vee(\sim q \wedge r)) (=(p \wedge(\sim q \vee r)) \wedge(\sim q \wedge r)) (=p \wedge(\sim q \wedge r)=p \wedge(\sim q) \wedge r)

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