# Set notation

### Set notation

#### Lessons

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
Introduction to Set Notation: 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.
Understanding How to Use Set Notation

Consider the following information:

- Universal set $U$ = {$0, 1, 2, 3, 4, 5, ...$}

- Set $N$ = {all natural numbers}

- Set $A$ = {$0$}

- Set $B$ = { }

a)
Is set $N$ a finite set or an infinite set? What about set $B$?

b)
List all disjoint sets, if any.

c)
Determine n(N), n(A) if possible.

d)
Patsy made a statement saying that n(A) = n(B). Is this true?

e)
Is the statement N $\subset$ U true?

• 4.
Consider the following Venn Diagram:

- Universal set $U =$ {archery, eating, chess, darts, soccer, basketball, football, volleyball, badminton}

- Set $A =$ {archery, eating, chess, darts}

- Set $B =$ {soccer, basketball, football, volleyball}

a)
Explain what the sets A and B represent.

b)
List all disjoint sets, if any.

c)
List all the elements of $B'$.

d)
Show that n(A) + n(A') = n(U).

• 5.
Consider the following Venn Diagram:

a)
What is the universal set?

b)
List all the elements in set A and B.

c)
Find a subset for set B.

d)
List all disjoint sets, if any.

e)
Find n(A), n(B), and n(C).

f)
Is set C a finite set?

• 6.
Drawing and Interpreting Venn Diagrams

Consider the following information:

- Universal Set $U =$ {-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).