XOR gate and its application in staircase light control

On comparing the AOI and XOR gate logic implementation, XOR logic results in a lower gate count and a reliable system.
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A certain system contains two identical circuits operating in parallel. As long as both are operating properly, the outputs of both circuits are always the same. If one of the circuits fails, the outputs will be at opposite levels at the same time. Which gate would you choose to detect that a failure has occurred in one of the circuit?
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If one of the inputs of a 2-input XOR gate is tied to Vcc (+5 V), the XOR behaves as:
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If one of the inputs of a 2-input XOR gate is connected to ground (0 V), the XOR:
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Can XOR gate be used to compare the parity (no. of 1’s) of the input applied?
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