MYP Standard Mathematics Venn Diagrams Key Definitions

The set of elements not in a set. The complement of $A$ (relative to $U$) is $A'$.

For any sets $A$ and $B$ in a universal set $U$,
$$(A \cup B)' = A' \cap B' \quad\text{and}\quad (A \cap B)' = A' \cup B'.$$

Two sets $A$ and $B$ are disjoint if they have no elements in common, so $A \cap B = \varnothing$.

Written $\emptyset$, is the set with no elements.

The set of elements that are in both sets. For sets $A$ and $B$, the intersection is $A \cap B$.

A set $A$ is a subset of $B$ (written $A\subseteq B$) if every element of $A$ is also an element of $B$.

The set of elements that are in at least one of the sets. For sets $A$ and $B$, the union is $A \cup B$.

The set of all elements being considered in a given situation, usually drawn as a rectangle and often labelled $U$.