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I came to the same result.
When there are only 2 inputs A and B, you can also build a truth table to show that (((A & B) ^ (A | B)) & (A ^ B)) = A ^ B ;)
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AND xor OR
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I came to the same result. When there are only 2 inputs A and B, you can also build a truth table to show that (((A & B) ^ (A | B)) & (A ^ B)) = A ^ B ;)