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NTA Abhyas 2020

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

NTA Abhyas 2020 · Mathematics · Mathematical Reasoning

The negation of p ∧ ( q → ∼ r ) is

The negation of

p ∧ ( q \to ∼ r )

is

Options

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

Correct answer

D. $∼ p ∨ ( q ∧ r )$

Step-by-step solution

∼ \left(p ∧ \left(q \to ∼ r\right)\right) = ∼ p ∨ \left(∼ \left(q \to ∼ r\right)\right)

( ∵ ( p ∧ q ) = p ∨ q & ( p \to q ) = p ∧ q )

= ∼ p ∨ ( q ∧ ∼ ( ∼ r ) )

= \sim p \lor ( q \land r )<br />&

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