Which one of the following Boolean expression | vedclass

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(D) tautology is a statement that is always true for all possible truth values of its components.Let us evaluate option $(A)$: $(p \vee q) \wedge (p \

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$(p \vee q) \vee (p \vee \sim q)$

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(D) tautology is a statement that is always true for all possible truth values of its components.Let us evaluate option $(A)$: $(p \vee q) \wedge (p \vee \sim q) \equiv p \vee (q \wedge \sim q) \equiv p \vee F \equiv p$. This is not a tautology.Let us evaluate option $(B)$: $(p \wedge q) \vee (p \wedge \sim q) \equiv p \wedge (q \vee \sim q) \equiv p \wedge T \equiv p$. This is not a tautology.Let us evaluate option $(C)$: $(p \vee q) \wedge (\sim p \vee \sim q) \equiv (p \vee q) \wedge \sim (p \wedge q)$. This is not a tautology.Let us evaluate option $(D)$: $(p \vee q) \vee (p \vee \sim q) \equiv p \vee (q \vee \sim q) \equiv p \vee T \equiv T$. Since the result is always true,this is a tautology.

Which one of the following Boolean expressions is a tautology?

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