Exclusive or

Exclusive or (Xor) is a binary operation where exactly on of the inputs needs to be true

$$x \oplus y = \begin{cases} \mbox{True} & \mbox{if } x \neq y\\ \mbox{False} & \mbox{if } x = y\end{cases}$$

it can be expressed as

$$x \oplus y = (x \lor y) \land (\lnot x \lor \lnot y).$$