# 13 Sets Summary

Set: A set is a collection of real or virtual objects called elements. Elements are written inside curly brackets. We write $A =$ {list of objects}.

Element: If $e$ is an element of $A$ we write $e \in A$.

Universal Set: The set of all elements that exist in the problem space.

Null Set: A null set is a set with no elements. It has the symbol $\emptyset$

Subset: $A$ is a subset of $B$ iff every element in $A$ exists in $B$. We write $A \subseteq B$

Proper Subset: $A$ is a proper subset of $B$ iff every element of $A$ exists in $B$ and there is at least one element in $B$ that is not in $A$. We write $A \subset B$

Union: The union of two sets, $A$ and $B$, contains all the elements of $A$ and all the elements of $B$. We write $A \cup B$

Intersection: The intersection of two sets, $A$ and $B$, is the set that contains all the elements of $A$ which are also in $B$. We write $A \cap B$

Universal Set: The set of all elements in the problem space.

Complement: The complement of $A$ is the set of all elements that are not in $A$.
We write $A' =$ {all the elements in the universal set that are not in $A$}