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(D) To determine which statement is a tautology,we construct a truth table for each statement pattern.$A$ statement is a tautology if its truth value

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$S_2$

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(D) To determine which statement is a tautology,we construct a truth table for each statement pattern.$A$ statement is a tautology if its truth value is $T$ for all possible combinations of truth values of its component statements.For $S_2 \equiv [p \wedge (p$ $\rightarrow q)]$ $\rightarrow q$:| $p$ | $q$ | $p \rightarrow q$ | $p \wedge (p \rightarrow q)$ | $[p \wedge (p$ $\rightarrow q)]$ $\rightarrow q$ ||---|---|---|---|---|| $T$ | $T$ | $T$ | $T$ | $T$ || $T$ | $F$ | $F$ | $F$ | $T$ || $F$ | $T$ | $T$ | $F$ | $T$ || $F$ | $F$ | $T$ | $F$ | $T$ |Since all entries in the final column for $S_2$ are $T$,$S_2$ is a tautology.

Which of the following statement patterns is a tautology?
$S_1 \equiv (\sim q \wedge p) \wedge q$
$S_2 \equiv [p \wedge (p$ $\rightarrow q)]$ $\rightarrow q$
$S_3 \equiv (p \wedge q) \wedge (\sim p \vee \sim q)$
$S_4 \equiv (p \wedge q) \rightarrow r$

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Which of the following statement patterns is a tautology?$S_1 \equiv (\sim q \wedge p) \wedge q$$S_2 \equiv [p \wedge (p$ $\rightarrow q)]$ $\rightarrow q$$S_3 \equiv (p \wedge q) \wedge (\sim p \vee \sim q)$$S_4 \equiv (p \wedge q) \rightarrow r$