The binary operator $\neq$ is defined by the following truth table. Which one of the following is true about the binary operator $\neq$?

The given truth table defines the exclusive-OR (XOR) operation, denoted by $\oplus$ or $\neq$, where the result is $1$ if and only if the inputs differ:

• Commutativity:

  $$p \neq q = q \neq p$$

  Since $0 \neq 0 = 0$, $1 \neq 1 = 0$, and $0 \neq 1 = 1 \neq 0 = 1$, the operator is commutative.

• Associativity:

  $$(p \neq q) \neq r = p \neq (q \neq r)$$

  The XOR operation on multiple inputs yields $1$ if and only if an odd number of inputs are $1$. Hence, the grouping of operands does not affect the outcome, so the operator is associative.

Therefore, the operator is both commutative and associative, corresponding to option (A).