Which of the following logic operations is performed by the following given…

Concept: NOR is a universal gate — every Boolean function, including EXCLUSIVE-OR, can be realized from a network of NOR gates. A common realization computes an intermediate signal A that is the NOR of the two inputs, then combines each input with A through two more NOR gates to isolate the two minterms of XOR (x·y′ and x′·y), and finally combines those two terms with a plain OR gate.

Gate identification: a gate drawn with a single concave (OR-shaped) body and a small bubble on its output is a NOR gate, not an XNOR gate — an XOR/XNOR-family gate shows an extra curved line just before the inputs, which is absent here. The three bubbled gates in the diagram are therefore NOR gates, and the final gate (same OR-shaped body, no bubble) is a plain OR gate.

Applying this to the given circuit:

1. The leftmost gate takes x and y and produces A = NOR(x, y), i.e. A = 1 only when x = y = 0.

2. The top middle gate takes x and A and produces B = NOR(x, A). By De Morgan's law, NOR(x, A) = x′·A′, and A′ = NOR(x,y)′ = x + y, so B = x′·(x + y) = x′·y.

3. The bottom middle gate takes y and A and produces C = NOR(y, A) = y′·A′ = y′·(x + y) = x·y′.

4. The rightmost gate is a plain OR, so f = B + C = x′y + xy′, which is exactly the sum-of-products form of EXCLUSIVE-OR.

Cross-check with the truth table: evaluating A, B, C and f for every input combination confirms f matches x XOR y in all four rows.

So the circuit performs the EXCLUSIVE-OR (XOR) operation on x and y.