Exclusive Disjunction

Definition: Exclusive Disjunction

The exclusive disjunction function is the Boolean operator $\mathrm{XOR}:\{0,1{\}}^2\to \{0,1\}$ defined in the following way:

$$\mathrm{XOR}(x,y)\stackrel{\text{def}}{=}\{\begin{array}{l}1\text{if }x\ne y\\ 0\text{otherwise}\end{array}$$

NOTATION

It is much more common to write $\mathrm{XOR}(x,y)$ in the following way:

$$x\oplus y$$