Consider the Boolean operator # with the following properties: $x\#0 = x$, $x\#1 = \bar{x}$, $x\#x = 0$ and $x\#\bar{x} = 1$. Then $x\#y$ is equivalent to

Given the properties of the operator $\#$:

1. $x \# 0 = x$

2. $x \# 1 = \bar{x}$

3. $x \# x = 0$

4. $x \# \bar{x} = 1$

These are precisely the characteristic properties of the exclusive-OR (XOR) operation $\oplus$:

• $x \oplus 0 = x$

• $x \oplus 1 = \bar{x}$

• $x \oplus x = 0$

• $x \oplus \bar{x} = 1$

The Boolean expression for XOR is:

Thus, option A is the correct answer.