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(D) statement pattern is a tautology if its truth value is $T$ for all possible combinations of truth values of its components.Based on the provided t

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$S_{4}$

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(D) statement pattern is a tautology if its truth value is $T$ for all possible combinations of truth values of its components.Based on the provided truth table:Column $9$ represents $S_{1} \equiv \sim p \rightarrow (q \leftrightarrow p)$. The values are $T, T, F, T$. Not a tautology.Column $10$ represents $S_{2} \equiv \sim p \vee \sim q$. The values are $F, T, T, T$. Not a tautology.Column $11$ represents $S_{3} \equiv (p$ $\rightarrow q) \wedge (q$ $\rightarrow p)$. The values are $T, F, F, T$. Not a tautology.Column $12$ represents $S_{4} \equiv (q \rightarrow p) \vee (\sim p \leftrightarrow q)$. The values are $T, T, T, T$.Since all entries in column $12$ are $T$,$S_{4}$ is a tautology.

Which of the following statement patterns is a tautology?
$S_{1} \equiv \sim p \rightarrow (q \leftrightarrow p)$
$S_{2} \equiv \sim p \vee \sim q$
$S_{3} \equiv (p$ $\rightarrow q) \wedge (q$ $\rightarrow p)$
$S_{4} \equiv (q \rightarrow p) \vee (\sim p \leftrightarrow q)$

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If the truth value of the compound statement $[(p \leftrightarrow q) \land (q \to r) \land \sim r] \to (p \land \sim q)$ is false, then the truth values of the statement patterns $(p \to q) \leftrightarrow (q \to r)$ and $\sim (p \lor r) \to (q \land p)$ are, respectively ...

The statement $(p \wedge q) \Rightarrow (p \wedge r)$ is equivalent to:

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Which of the following statement patterns is a tautology?$S_{1} \equiv \sim p \rightarrow (q \leftrightarrow p)$$S_{2} \equiv \sim p \vee \sim q$$S_{3} \equiv (p$ $\rightarrow q) \wedge (q$ $\rightarrow p)$$S_{4} \equiv (q \rightarrow p) \vee (\sim p \leftrightarrow q)$