Right Answer is:
$\overline{X+Y}$
SOLUTION
Since 1, 2 & 3 are grounded.
S1 | S0 | V |
0 | 0 | I0 |
0 | 1 | I1 |
1 | 0 | I2 |
1 | 1 | I3 |
I0 = 1, I1 = 0, I2 = 0, I3 = 0
x = S2
y = S1
The output of the 4 x 1 MUX is:
$Y = F = \bar{S_1}\bar{S_2}I_0 + \bar{S_1}S_2I_1 + S_1\bar{S_2}I_2 + S_1S_2I_3$
Substituting the values:
$F = xy \cdot 1 + xy \cdot 0 + xy \cdot 0 + xy \cdot 0$
Simplifying:
$F =\bar{X}\bar{Y} = \overline{X+Y}$