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Outputs of the intermediate NOT gates:
$$\text{Inputs to top AND gate} = A \text{ and } \bar{B}$$
$$\text{Inputs to bottom AND gate} = \bar{A} \text{ and } B$$
Output of the final OR gate:
$$Y = (A \cdot \bar{B}) + (\bar{A} \cdot B)$$
$$Y = A \oplus B \quad (\text{XOR gate operation})$$
XOR gate gives high output for Odd number of $$1s$$
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