Question:
The statement $A \rightarrow(B \rightarrow A)$ is equivalent to :
Correct Option: , 4
Solution:
$\mathrm{A} \rightarrow(\mathrm{B} \rightarrow \mathrm{A})$
$\equiv \mathrm{A} \rightarrow(\sim \mathrm{B} \vee \mathrm{A})$
$\equiv \sim \mathrm{A} \vee(\sim \mathrm{B} \vee \mathrm{A})$
$\equiv(\sim \mathrm{A} \vee \mathrm{A}) \vee \sim \mathrm{B}$
$\equiv \mathrm{T} \vee \sim \mathrm{B} \equiv \mathrm{T}$
$\therefore \mathrm{T} \vee \mathrm{B}=\mathrm{T}$
$\equiv(\sim \mathrm{A} \vee \mathrm{A}) \vee \mathrm{B}$
$\equiv \sim \mathrm{A} \vee(\mathrm{A} \vee \mathrm{B})$
$\equiv \mathrm{A} \rightarrow(\mathrm{A} \vee \mathrm{B})$