# Logical OR

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Previous lesson: Logical AND

## The Disjunction

I apologize for the name of this lesson. The true name of this operator, which is a diadic operator, is a **disjunction**. It is sometimes called the **inclusive OR operator**, to distinguish it from another operator you'll learn about later. However, it is a bit dangerous to refer to a disjunction as an OR operator, because English words are far more vague than logic.

[math]\vee[/math] : This is the disjunction, a.k.a. the (inclusive) OR operator

- Let [math]p[/math] represent the statement: It is raining.
- Let [math]q[/math] represent the statement: I am hungry.
- [math]p \vee q[/math] represents the disjunction of statements [math]p[/math] and [math]q[/math]: It is raining OR I am hungry (OR it is raining AND I am hungry).

## Truth Table for the Disjunction

This is its truth table:

[math]p \,\![/math] | [math]q \,\![/math] | [math]p \vee q[/math] |
---|---|---|

T | T | T |

T | F | T |

F | T | T |

F | F | F |

## Next Lesson

The name of the next lesson is Logical XOR.