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:

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

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

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

${A}^{C}=\left\{\text{allrealnumbersexcept}1,2,3\text{and}4\right\}$

**
Example 2:**

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

Then:

$\begin{array}{l}A\cap B=\left\{y,z\right\}\\ A\cup B=\left\{x,y,z\right\}\\ A-B=\varnothing \\ {A}^{C}=\left\{\text{everythingexcept}y\text{and}z\right\}\end{array}$