The statement among the following that is a tautology is:
Question:

The statement among the following that is a tautology is:

1. (1) $A \wedge(A \vee B)$

2. (2) $\mathrm{B} \rightarrow[\mathrm{A} \wedge(\mathrm{A} \rightarrow \mathrm{B})]$

3. (3) $A \vee(A \wedge B)$

4. (4) $[\mathrm{A} \wedge(\mathrm{A} \rightarrow \mathrm{B})] \rightarrow \mathrm{B}$

Correct Option: , 4

Solution:

$A \wedge(\sim A \vee B) \rightarrow B$

$=[(A \wedge \sim A) \vee(A \wedge B)] \rightarrow B$

$=(A \wedge B) \rightarrow B$

$=\sim A \vee \sim B \vee B$

$=t$