The given circuit, with the output of the respective gates is as given below.
The Boolean expression of the output is Y=(A⋅B)⋅(A+B) ⇒Y=(A+B)⋅(A+B) (using de-Morgan's theorem, x⋅y=x+y ) ⇒Y=A⋅B+B⋅A This represents the Boolean expression for XOR gate. Alternate solution This question can also be verified from the following truth table.
A
B
P=A⋅B
Q=A+B
Y=P⋅Q
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
Hence, the output of this circuit represents the output of a XOR gate.