Logical XOR

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!

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.