> For the complete documentation index, see [llms.txt](https://adams-personal-organization.gitbook.io/compendium-of-predicates/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://adams-personal-organization.gitbook.io/compendium-of-predicates/definitions/complement.md).

# Complement

<details>

<summary><span class="math">\textbf{Complement} \; A \; B \; R := \top_{A,B} - R</span></summary>

***

$$\textbf{Relation} ; A ; B ; R$$

***

**Notation.**

1. $$\textbf{Complement} ; A ; B ; R$$ can be written $$\textbf{Complement} ; R$$ when $$A$$ and $$B$$are clear from the context.
2. $$\textbf{Complement} ; R$$ can be written symbolically as $$\neg R$$ or $$\overline{R}$$.

***

```
fun Co(A,B: set univ, R: A->B) : A->B {
  (A->B) - R
}
```

</details>