---
tags:
  - Logic
  - propositional-logic
  - derivation-rules
---

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*.

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