Here AND gate is performed as intersection operations as it will return common elements between $f_1,f_2$
OR gate is performed as a union operation as it will return all the elements present in both $f_3,f_4$
Assume the output of the AND gate is $y_1$ and the output of the OR gate is $y_2$.
$y_1=f_1.f_2=\sum_m(3,5,7,11,13)$
$y_2=f3+f_4=\sum_m(0,1,2,4,6,11,13)$
Now both $y_1,y_2$ act as input for XOR gate which returns the elements that is in either in $y_1$ or in $y_2$. It will discard the common elements between $y_1,y_2$.
So the output $Y=y_1\oplus y_2=\sum_m(0,1,2,3,4,5,6,7) \equiv \Pi_m(8,9,10,11,12,13,14,15)$
So Option $(C, D)$ is correct.
A similar type of concept asked in:
- GATE CSE 2002 | Question: 2-1
- GATE CSE 2008 | Question: 8
- GATE CSE 2020 | Question: 28