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(D) To check if the statement $[A \wedge (A$ $\rightarrow B)]$ $\rightarrow B$ is a tautology,we simplify it using logical laws:$[A \wedge (A$ $\right

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$[A \wedge (A$ $\rightarrow B)]$ $\rightarrow B$

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(D) To check if the statement $[A \wedge (A$ $\rightarrow B)]$ $\rightarrow B$ is a tautology,we simplify it using logical laws:$[A \wedge (A$ $\rightarrow B)]$ $\rightarrow B$$= [A \wedge (\sim A \vee B)] \rightarrow B$$= [(A \wedge \sim A) \vee (A \wedge B)] \rightarrow B$$= [F \vee (A \wedge B)] \rightarrow B$$= (A \wedge B) \rightarrow B$$= \sim (A \wedge B) \vee B$$= (\sim A \vee \sim B) \vee B$$= \sim A \vee (\sim B \vee B)$$= \sim A \vee T$$= T$Since the final result is $T$ (a tautology),the statement $[A \wedge (A$ $\rightarrow B)]$ $\rightarrow B$ is a tautology.

The statement among the following that is a tautology is

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Among the statements:
$(S1): (p \Rightarrow q) \vee ((\sim p) \wedge q)$ is a tautology
$(S2): (q \Rightarrow p) \Rightarrow ((\sim p) \wedge q)$ is a contradiction