Discussion
Which one of the following is NOT a valid identity ?
Answer: B
The identity that is not valid is (x+y)⊕z = x⊕(y+z).
Take x = 1, y = 1, z = 0. The left side is (1 + 1)⊕0 = 1⊕0 = 1, while the right side is 1⊕(1 + 0) = 1⊕1 = 0. The two sides differ, so OR and XOR cannot be regrouped this way.
The others hold: XOR is associative; when xy = 0 the two inputs are never both 1, so XOR equals OR; and x⊕y is the complement of XNOR, (xy + x'y')'.
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