# Operations on Sets

Recall that a set is a collection of elements.

Given sets $A$ and $B$, we can define the following operations:

 Operation Notation Meaning Intersection $A\cap B$ all elements which are in both $A$ and $B$ Union $A\cup B$ all elements which are in either $A$ or $B$(or both) Difference $A-B$ all elements which are in $A$ but not in $B$ Complement $\overline{A}$ (or ${A}^{C}$) all elements which are not in $A$

Example 1:

Let $A=\left\{1,2,3,4\right\}$ and let $B=\left\{3,4,5,6\right\}$.

Then:

$A\cap B=\left\{3,4\right\}$

$A\cup B=\left\{1,2,3,4,5,6\right\}$

$A-B=\left\{1,2\right\}$

Example 2:

Let $A=\left\{y,z\right\}$ and let $B=\left\{x,y,z\right\}$.

Then: