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!

$\oplus$ : 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 $p$ represent the statement: It is raining.

Let $q$ represent the statement: I am hungry.

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

Truth Table

Its truth table is unique. Here it is!

$p\,\!$	$q\,\!$	$p\oplus q$
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.