Question:
The statement $\mathrm{A} \rightarrow(\mathrm{B} \rightarrow \mathrm{A})$ is equivalent to:
Correct Option: , 2
Solution:
$A \rightarrow(B \rightarrow A)$
$\Rightarrow \mathrm{A} \rightarrow(\sim \mathrm{B} \vee \mathrm{A})$
$\Rightarrow \sim A \vee(\sim B \vee A)$
$\Rightarrow \sim B \vee(\sim A \vee A)$
$\Rightarrow \sim B \vee t$
$=\mathrm{t}$ (tautology) From options:
(2) $\mathrm{A} \rightarrow(\mathrm{A} \vee \mathrm{B})$
$\Rightarrow \sim A \vee(A \vee B)$
$\Rightarrow(\sim A \vee A) \vee B$
$\Rightarrow t \vee B$
$\Rightarrow t$