The negation of p ∧ ( q → ∼ r ) is

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Question: Answered & Verified by Expert

The negation of

p \land (q \to \sim r)

is

MathematicsMathematical ReasoningJEE Main

Options:

A $\sim p \land (q \land r)$
B $p \lor (q \lor r)$
C $p \lor (q \land r)$
D $\sim p \lor (q \land r)$

Solution:

2790 Upvotes Verified Answer

The correct answer is:

\sim p \lor (q \land r)

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

(∵ ~ (p \land q) = ~ p \lor ~ q & ~ (p \to q) = p \land ~ q)

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

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

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