**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 $A$}**