Set notation - Set Theory

Set notation

Lessons

Notes:

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 $\overline{B}$ .

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 $B$ = { }
4.
Consider the following Venn Diagram:
- Universal set $U = \{\mathrm{archery, eating, chess, darts,soccer, basketball, football, volleyball, tennis, badminton}\}$
- Set $A = \{\mathrm{archery, eating, chess, darts}\}$
- Set $B = \{\mathrm{soccer, basketball, football, volleyball}\}$
5.
Consider the following Venn Diagram:
6.
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}

Set notation

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Intro Lesson

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Intro

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Don't just watch, practice makes perfect

Do better in math today

Don't just watch, practice makes perfect

Lessons

Notes:

Intro Lesson

Set Notations Overview: Definitions and Terms

1.

Drawing Venn Diagrams With Sets Consider the following information: AAA = {1, 2, 3} BBB = {3, 4, 5} Universal Set UUU = {1, 2, 3, 4, 5, 6, 7} Draw a Venn Diagram describing the 3 sets.

2.

Consider the following information: AAA = {1, 2, 3} BBB = {4, 5, 6} Universal Set UUU = {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 UUU = {0, 1, 2, 3, 4, 5,...} Set NNN = {all natural numbers} Set AAA = {0} Set BBB = { }

a)

Is set NNN a finite set or an infinite set? What about set BBB ?

b)

List all disjoint sets, if any.

c)

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

d)

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

e)

Is the statement N⊂UN \subset UN⊂U true?

4.

a)

Explain what the sets A,BA,BA,B and UUU represent.

b)

List all disjoint sets, if any.

c)

List all the elements of B′B'B′ .

d)

Show that n(A)+n(A′)=n(U)n(A)+n(A')=n(U)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 AAA and BBB.

c)

Find a subset for set BBB.

d)

or

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.

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.

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 $B$ = { }

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

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

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

Is the statement $N \subset U$ true?

Explain what the sets $A,B$ and $U$ represent.

List all the elements of $B'$ .

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

List all the elements in set $A$ and $B$ .

Find a subset for set $B$ .

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

Is set $C$ a finite set?

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