From the given options, the truth values of p,q and r respectively for which ( p ∧ q ) ∨ ( ∼ r ) has a truth value F are Options: A . &nbsp F, F, F B . &nbsp T, T, T C . &nbsp T, F, F D . &nbsp F, F, T

From the given options, the truth values of p,q and r respectively for which (

Discussion Forum : Mathematical Reasoning

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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

Options:

A . F, F, F

B . T, T, T

C . T, F, F

D . F, F, T

Answer: Option D
:
D

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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