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categories:
  - Logic
tags: []
---

# Disjunction Introduction

This rule can seem a little odd: like we are randomly introducing an additional proposition without giving any justification. However this is just a consequence of the fact if $P$ is true, so is $P \lor Q$ since disjunction is not the same as conjunction: only one disjunct needs to be true for the compound disjunction to be true. This is represented in the context of [truth-trees](Truth-trees.md#disjunction-decomposition) by the fact that truth can pass up via either branch of a disjunction pattern.
This rule is sometimes also referred to (confusingly) as _Addition_.

![](/_img/disjunc-intro.png)
