Question:
The statement among the following that is a tautology is :
Correct Option: , 4
Solution:
$(\mathrm{A} \wedge(\mathrm{A} \rightarrow \mathrm{B})) \rightarrow \mathrm{B}$
$=(A \wedge(\sim A \vee B)) \rightarrow B$
$=((A \wedge \sim A) \vee(A \wedge B)) \rightarrow B$
$=(A \wedge B) \rightarrow B$
$=\sim(A \wedge B) \vee B$
$=(\sim A \vee \sim B) \vee B$
$=T$
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