# Set notation

### Set notation

#### Lessons

In this lesson, we will learn:

• Drawing Venn Diagrams With Sets
• Understanding How to Use Set Notation
• Drawing and Interpreting Venn Diagrams

Notes:

Here are some terms that we need to know for set notations:

Set: A list of objects or numbers.

Element: An object or a number in a set.

n($A$): The number of elements in set $A$.

Subset: A set where all its elements belong to another set.

Universal Set: A set of all elements in a particular context.

Empty Set: A set with no elements.

Disjoint: Two or more sets that do not have any elements in common.

Mutually Exclusive: Two or more events that cannot happen simultaneously.

Finite Set: A set with a finite number of elements.

Infinite Set: A set with an infinite number of elements.

Complement: The list of remaining elements in the universal set that is not in the mentioned set. If $B$ is a set. Then we defined the complement to be $B'$ or $\overline{B}$.

• Introduction
Set Notations Overview: Definitions and Terms

• 1.
Drawing Venn Diagrams With Sets

Consider the following information:

• $A$ = {1, 2, 3}
• $B$ = {3, 4, 5}
• Universal Set $U$ = {1, 2, 3, 4, 5, 6, 7}

Draw a Venn Diagram describing the 3 sets.

• 2.

Consider the following information:

• $A$ = {1, 2, 3}
• $B$ = {4, 5, 6}
• Universal Set $U$ = {1, 2, 3, 4, 5, 6, 7}

Draw a Venn Diagram describing the 3 sets.

• 3.
Drawing and Interpreting Venn Diagrams

Consider the following information:

• Universal Set $U =$ $\mathrm\{-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$
• Set $A$ = {positive odd number up to 10}
• Set $B$ = {positive even number up to 10}
• Set $C$ = {0}
a)
Draw a Venn diagram

b)
List all disjoint sets, if any.

c)
Find $n(A)$, $n(B)$, and $n(C)$.