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Negation

From the give...

Question

From the given options, the truth values of p,q and r respectively for which $(p \land q) \lor (\sim r)$ has a truth value F are

F, F, F

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T, T, T

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T, F, F

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F, F, T

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Solution

The correct option is D
F, F, T

Given that $(p \land q) \lor (\sim r)$ is false.
$∴ i) (p \land q) i s f a l s e i i) \sim r i s f a l s e (p \land q) i s f a l s e$
Hence, p and q cannot be true simulaneously.
Also, ~r is false. Hence, r must be true.

Only option D satisfies this condition

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