$A$ |
$B$ |
$f_0$ |
$f_1$ |
$f_2$ |
$f_3$ |
$f_4$ |
$f_5$ |
$f_6$ |
$f_7$ |
$f_8$ |
$f_9$ |
$f_{10}$ |
$f_{11}$ |
$f_{12}$ |
$f_{13}$ |
$f_{14}$ |
$f_{15}$ |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
1 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
As we can see from the above table ,
Using $n$ boolean variables (here $n=2$ $A,B$ are boolean variables),
We can create $2^n$ combinations ($00,01,10,11$)
and using those $2^n$ combinations we can create $2^{2^n}$ functions ($16$ functions = $f_0,f_1,....f_{15}$)
$\therefore$ Option $1.$ is correct.