Set notation - Set Theory

Set notation

Lessons

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

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

- Set $B =$ {soccer, basketball, football, volleyball}
5.
Consider the following Venn Diagram:
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}

Set notation

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Lessons

Notes:

Intro Lesson

Introduction to Set Notation: Definitions and Terms

1.

Drawing Venn Diagrams With Sets Consider the following information: - A=A =A= {1,2,31, 2, 31,2,3} - B=B=B= {3,4,53, 4, 53,4,5} - Universal Set UUU = {1,2,3,4,5,6,71, 2, 3, 4, 5, 6, 71,2,3,4,5,6,7} Draw a Venn Diagram describing the 3 sets.

2.

Consider the following information: - AAA = {1,2,31, 2, 31,2,3} - BBB = {4,5,64, 5, 64,5,6} - Universal Set UUU = {1,2,3,4,5,6,71, 2, 3, 4, 5, 6, 71,2,3,4,5,6,7} 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,...0, 1, 2, 3, 4, 5, ...0,1,2,3,4,5,...} - Set NNN = {all natural numbers} - Set AAA = {000} - 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(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=U =U= {archery, eating, chess, darts, soccer, basketball, football, volleyball, badminton} - Set A=A =A= {archery, eating, chess, darts} - Set B=B =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′B'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)

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 $B$ ?

Is the statement N $\subset$ U true?

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}

List all the elements of $B'$ .

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}