The statement among the following that is a tautology is :

Question:

The statement among the following that is a tautology is :

 

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

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

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

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


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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