Which of the following is not a tautology?

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(D) statement is a tautology if its truth value is always $T$ (True) for all possible truth values of its components.$1$. For $(p$ $\Rightarrow q) \we

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None of these

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(D) statement is a tautology if its truth value is always $T$ (True) for all possible truth values of its components.$1$. For $(p$ $\Rightarrow q) \wedge p$ $\Rightarrow q$:$(\sim p \vee q) \wedge p$ $\Rightarrow q = ((\sim p \wedge p) \vee (q \wedge p))$ $\Rightarrow q = (F \vee (p \wedge q))$ $\Rightarrow q = (p \wedge q)$ $\Rightarrow q = \sim (p \wedge q) \vee q = \sim p \vee \sim q \vee q = \sim p \vee T = T$.$2$. For $(p \vee q) \wedge (\sim p) \Rightarrow q$:$((p \wedge \sim p) \vee (q \wedge \sim p))$ $\Rightarrow q = (F \vee (q \wedge \sim p))$ $\Rightarrow q = (q \wedge \sim p)$ $\Rightarrow q = \sim (q \wedge \sim p) \vee q = \sim q \vee p \vee q = T \vee p = T$.$3$. For $(p$ $\Rightarrow q) \wedge (q$ $\Rightarrow r)$ $\Rightarrow (p$ $\Rightarrow r)$:This is the standard law of hypothetical syllogism,which is a tautology.Since all the given statements are tautologies,the correct answer is 'None of these'.

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