---
tag: 0KCT6DPXJK
kind: concept
name: Venn diagram
msc: ["03E20"]
uses: [07KVB4JSC7, 0HBRW4E6G1, 0B1FSS1VZW]
sources:
  - url: https://en.wikipedia.org/wiki/Venn_diagram
    locator: lead section
same_as:
  wikidata: Q190763
  wikipedia: Venn diagram
---

## Summary

A Venn diagram is a picture of the relations between a small number of sets.
Each set is a closed curve, often a circle, inside a rectangle for the [[universal set|0BPYRMHJ48]].
For $n$ sets, the curves cut the plane into $2^n$ regions, one for each combination of "in" and "out" of the sets.

## Remarks

John Venn made these diagrams popular in the 1880s.
The diagrams make laws such as [[De Morgan's laws for sets|0VK0W4D5Y5]] visible, but a picture is not a proof.
An Euler diagram is similar, but it shows only the regions that are not empty.

## Explanations

### L1 human

Draw two overlapping circles $A$ and $B$.
The overlap is $A \cap B$, both circles together are $A \cup B$, and the region outside both circles is the complement of $A \cup B$.