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Which one of the following Boolean expressions is a tautology?
$\left( {p \vee q} \right) \wedge \left( {p \vee \sim q} \right)$
$\left( {p \wedge q} \right) \vee \left( {p \wedge \sim q} \right)$
$\left( {p \vee q} \right) \wedge \left( { \sim p \vee \sim q} \right)$
$\left( {p \vee q} \right) \vee \left( {p \vee \sim q} \right)$
Solution
From options
$\left( {p \vee q} \right) \wedge \left( { \sim p \vee \sim q} \right) = \left( {p \vee q} \right) \wedge \sim \left( {p \wedge q} \right) \to $ Not a tautology
$\left( {p \vee q} \right) \vee \left( {p \vee \sim q} \right) = p \wedge \left( {q \vee \sim q} \right) \to $ tautology
$\left( {p \wedge q} \right) \vee \left( {p \wedge \sim q} \right) \equiv p \wedge \left( {q \vee \sim q} \right) \to $ Not a tautology
$\left( {p \vee q} \right) \wedge \left( {p \wedge \sim q} \right) \equiv p \vee \left( {q \wedge \sim q} \right) \to $ Not a tautology
