---
tags:
  - propositional-logic
  - logic
---

# 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)
