Which one of the following is a tautology?

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(D) tautology is a statement that is always true for all possible truth values of its components.$1$. For $P \wedge (P \vee Q) \equiv P$,which is not

Vedclass · Accepted Answer

$(P \wedge (P$ $\rightarrow Q))$ $\rightarrow Q$

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(D) tautology is a statement that is always true for all possible truth values of its components.$1$. For $P \wedge (P \vee Q) \equiv P$,which is not a tautology.$2$. For $P \vee (P \wedge Q) \equiv P$,which is not a tautology.$3$. For $Q$ $\rightarrow (P \wedge (P$ $\rightarrow Q)) \equiv Q$ $\rightarrow (P \wedge (\sim P \vee Q)) \equiv Q$ $\rightarrow (P \wedge Q) \equiv \sim Q \vee (P \wedge Q) \equiv (\sim Q \vee P) \wedge (\sim Q \vee Q) \equiv (\sim Q \vee P) \wedge t \equiv \sim Q \vee P$,which is not a tautology.$4$. For $(P \wedge (P$ $\rightarrow Q))$ $\rightarrow Q \equiv (P \wedge (\sim P \vee Q))$ $\rightarrow Q \equiv (P \wedge Q)$ $\rightarrow Q \equiv \sim (P \wedge Q) \vee Q \equiv (\sim P \vee \sim Q) \vee Q \equiv \sim P \vee (\sim Q \vee Q) \equiv \sim P \vee t \equiv t$.Since the result is $t$ (true),option $D$ is a tautology.

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