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If q is false and $p \land q \leftrightarrow r$ is true then which one of the following statements is a tautology ?

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$(p \lor r) \to (p \land r)$

$(p \land r) \to (p \lor r)$

$p \land r$

$p \lor r$

answer is B.

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Detailed Solution

$q is F then p \land q is F$

$p \land q \leftrightarrow r is T then r is F$

$p \lor r$ may be true or false and $p \land r$ is false

$(p \land r) \to (p \lor r)$ is a tautology

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