Which of the following is a tautology?

(\sim q \land p) \land q

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(\sim q \land p) \land (p \land \sim p)

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

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(p \land q) \land (\sim (p \land q))

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Solution

The correct option is C $(\sim q \land p) \lor (p \lor \sim p)$
$(\sim q \land p) \land q$
Using Set Theory approach,
$(Q^{c} \cap P) \cap Q = ϕ$
$(\sim q \land p) \land q$ is not a tautology.

$(\sim q \land p) \land (p \land \sim p)$
$(p \land \sim p)$ is always false.
$(\sim q \land p) \land F = F$
$(\sim q \land p) \land (p \land \sim p)$ is not a tautology.

$(\sim q \land p) \lor (p \lor \sim p)$
$(p \lor \sim p) = T$
$(\sim q \land p) \lor T = T$
$(\sim q \land p) \lor (p \lor \sim p)$ is a tautology.

$(p \land q) \land (\sim (p \land q))$ can be expressed as $a \land \sim a$ , which is always false, where $a = p \land q$ .
Therefore, $(p \land q) \land (\sim (p \land q))$ is not a tautology.

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