Venn diagram

From CS2800 wiki


One easy way to construct a set is to draw a picture of it. A common way of doing so is a Venn diagram such as this one:

Venn-diag.svg

This diagram indicates that the set [math]A [/math] consists of all of the points in the left-hand circle, while set [math]B [/math] consists of the points in the right hand circle.

Be careful: although Venn diagrams are a great way to create examples, they do not provide proofs that work for arbitrary sets. For example, an argument made using the diagram above does not describe the cases where [math]A \href{/cs2800/wiki/index.php/%5Csubseteq}{\subseteq} B [/math] or when [math]A \href{/cs2800/wiki/index.php/%5Ccap}{\cap} B \href{/cs2800/wiki/index.php/Equality_(sets)}{=} \href{/cs2800/wiki/index.php?title=%5Cemptyset&action=edit&redlink=1}{\emptyset} [/math]. Moreover, it doesn't consider finite sets or sets that are larger than any set of points in the plane. Venn diagrams give intuition (and examples) but not proofs.