Set Notation

This lesson covers:

  1. What 'sets' are 
  2. How to use set notation
  3. How to interpret Venn diagrams 

Set notation

Illustration showing set notation with numbers and shapes as elements in sets A and B.

A set is a collection of mathematical objects (e.g. numbers, symbols, points on a graph, shapes etc.) - we call each of these objects an 'element'.

In other words, a set is a group of elements.

We usually represent sets by placing the elements inside curly brackets { }.


For example, as the elements in set A (in the image above) are the numbers 22, 18, 0.5, and 6, then we could say 'set A = {22, 18, 0.5, 6}'.

n(A) refers to the number of elements in set A, so as there are 4 numbers in set A, we would say 'n(A) = 4'.

Venn diagrams


On a Venn diagram, each set is represented by a circle.

Diagram showing set A with elements 2.2, 18, 0.5, and 6 represented in a Venn diagram.

So Venn diagrams ca be used to show multiple sets at once, by showing multiple circles.


Around the circles is a rectangle, which represents the universal set- this is the set that contains all the elements in all the sets - it is denoted by the symbol 𝝽 (this is the greek letter 'Xi').

Venn diagram showing two sets, Set A and Set B, within a rectangle representing the universal set.

There are 6 common Venn diagram notations you need to know:


1A - everything in set A

Venn diagram showing sets A and B with a universal set represented by a rectangle.

2A' - everything NOT in Set A (the complement of A)

Venn diagram showing two overlapping circles representing sets A and B within a rectangle representing the universal set.

3A ⋂ B - A intersect B (everything in both) 

Venn diagram showing sets A and B with a universal set represented by a rectangle.

4(A ⋂ B)' - everything NOT in both

Venn diagram showing two sets A and B with their intersection highlighted inside a rectangle representing the universal set.

5A ⋃ B - A union B (everything in A OR B)

Venn diagram showing two sets A and B with a universal set represented by a rectangle.

6 (A ⋃ B)' - everything NOT in A union B

Venn diagram showing two sets A and B with a rectangle representing the universal set.

What is the correct set notation for the highlighted region in the Venn diagram below?

Venn diagram illustrating sets A and B with a highlighted region.

A ⋂ B 

(A ⋂ B)'

(A ⋃ B)' 

A ⋃ B 

0

/

1

What is the correct set notation for the highlighted region in the Venn diagram below?

Venn diagram showing sets A and B with highlighted overlapping region.

A ⋂ B 

A ⋃ B 

(A ⋃ B)' 

(A ⋂ B)'

0

/

1

Which set notation below means:


'A union B'

A ⋃ B 

(A ⋂ B)'

A ⋂ B 

(A ⋃ B)' 

0

/

1

What is the correct set notation for the highlighted region in the Venn diagram below?

Venn diagram highlighting the intersection of sets A and B.

B'

A'

B

A

0

/

1

Which set notation below means:


'A intersect B'

A ⋂ B 

(A ⋂ B)'

A ⋃ B 

(A ⋃ B)' 

0

/

1

What is the correct set notation for the highlighted region in the Venn diagram below?

Venn diagram showing sets A and B with the highlighted region representing set A.

A'

B'

B

A

0

/

1

What is the correct set notation for the highlighted region in the Venn diagram below?

Venn diagram showing two overlapping sets A and B with a highlighted intersection.

(A ⋂ B)'

A ⋃ B 

A ⋂ B 

(A ⋃ B)' 

0

/

1

What is the correct set notation for the highlighted region in the Venn diagram below?

Venn diagram showing set notation with highlighted region between sets A and B.

(A ⋃ B)' 

(A ⋂ B)'

A ⋂ B 

A ⋃ B 

0

/

1