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 $\overline{B}$ .

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.

- a)
  Definitions and Terms
- b)
  Drawing Venn Diagrams with Sets
- 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?
- a)
  Explain what the sets $A,B$ and $U$ represent.
- b)
  List all disjoint sets, if any.
- c)
  List all the elements of $B'$ .
- d)
  Show that $n(A)+n(A?)=n(C)$ .
3.
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

Don't just watch, practice makes perfect.

We have over 1850 practice questions in Algebra for you to master.

Get Started Now

Let's keep going.

Play next lesson

Let's learn the next topic

Let's keep going.

Play next lesson

Let's learn the next topic

Goto next topic

Let's keep going

Let's keep going!

Play next lesson or Practice this topic

Start now and get better math marks!

Keep exploring StudyPug

Start now and get better math marks!

Keep exploring StudyPug

Intro Lesson:

Selected

Lesson: 1

Lesson: 2

Lesson: 3a

Lesson: 3b

Lesson: 3c

Intro

Learn

Practice

Do better in math today

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:

a)

Definitions and Terms

b)

Drawing Venn Diagrams with Sets

1.

Consider the following information: Universal set U=0,1,2,3,4,5,...U = {0,1,2,3,4,5,...}U=0,1,2,3,4,5,... Set N=allnaturalnumbersN = {all natural numbers} N=allnaturalnumbers Set A=0A={0}A=0 Set B=B={ }B=

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?

2.

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(C)n(A)+n(A?)=n(C)n(A)+n(A?)=n(C) .

3.

Drawing and Interpreting Venn Diagrams Consider the following information: - Universal Set U=U =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).

Set notation

Don't just watch, practice makes perfect.

We have over 1850 practice questions in Algebra for you to master.

or

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 $n(A)+n(A?)=n(C)$ .

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}