Question

Prove or disprove that the exclusive or operation (⊕) is associative, i.e., A⊕(B⊕C)=(A⊕B)⊕C.

Answer 1

The exclusive OR (XOR) operation is not associative, and we can prove this using a counterexample.

Step-by-step explanation:

The exclusive OR (XOR) operation is not associative. We can prove this by providing a counterexample.

Let's consider the expression: A⊕(B⊕C).

Suppose A = 1, B = 0, and C = 1. Then, A⊕(B⊕C) = 1⊕(0⊕1) = 1⊕1 = 0.

Now, let's consider the expression: (A⊕B)⊕C.

If we use the same values for A, B, and C, we get (A⊕B)⊕C = (1⊕0)⊕1 = 1⊕1 = 0.

Since A⊕(B⊕C) = 0 and (A⊕B)⊕C = 0 for these values, we can conclude that the XOR operation is not associative.