# Logical XOR

 Type classification: this is a lesson resource.

Welcome! This is a lesson in the Introductory Discrete Mathematics for Computer Science course here at Wikiversity.

Previous lesson: Logical OR

## Introducing the Exclusive OR!

${\displaystyle \oplus }$ : This is the XOR operator. It is also called the exclusive OR, to distinguish it from the inclusive OR of the previous lesson. Like the inclusive OR, it is a dyadic operator; unlike any other operator, it is true when one and only one input is true.

Let ${\displaystyle p}$ represent the statement: It is raining.
Let ${\displaystyle q}$ represent the statement: I am hungry.
${\displaystyle p\oplus q}$ represents the exclusive disjunction of statements ${\displaystyle p}$ and ${\displaystyle q}$: It is raining OR I am hungry, But not both.

## Truth Table

Its truth table is unique. Here it is!

${\displaystyle p\,\!}$ ${\displaystyle q\,\!}$ ${\displaystyle p\oplus q}$
T T F
T F T
F T T
F F F

## Why XOR is Special

XOR is used for adding binary numbers, and is the fundamental arithmetic operation used by computers.

## Next Lesson

Your next lesson is called Conditional Operator.