Unit 1 Section 3 : Sets and Venn Diagrams

In this section we introduce the ideas of sets and Venn diagrams. A set is a list of objects in no particular order; they could be numbers, letters or even words. A Venn diagram is a way of representing sets visually.

To explain, we will start with an example where we use whole numbers from 1 to 10.
We will define two sets taken from this group of numbers:
Set A = the odd numbers in the group = { 1 , 3 , 5 , 7 , 9 }
Set B = the numbers which are 6 or more in the group = { 6 , 7 , 8 , 9 , 10 }

Some numbers from our original group appear in both of these sets. Some only appear in one of the sets.
Some of the original numbers don't appear in either of the two sets. We can represent these facts using a Venn diagram.
The two large circles represent the two sets.

The numbers which appear in both sets are 7 and 9. These will go in the central section, because this is part of both circles.

The numbers 1, 3 and 5 still need to be put in Set A, but not in Set B, so these go in the left section of the diagram.

Similarly, the numbers 6, 8 and 10 are in Set B, but not in Set A, so will go in the right section of the diagram.

The numbers 2 and 4 are not in either set, so will go outside the two circles.

The final Venn diagram looks like this:

We can see that all ten original numbers appear in the diagram.

The numbers in the left circle are Set A
{ 1 , 3 , 5 , 7 , 9 }

The numbers in the right circle are Set B
{ 6 , 7 , 8 , 9 , 10 }

In the rest of this section you will practise filling in Venn diagrams and using them.

The intersection of sets A and B is those elements which are in set A and set B. A diagram showing the intersection of A and B is on the left.

The union of sets A and B is those elements which are in set A or set B or both. A diagram showing the union of A and B is on the right.

Example

Work out the answer to each of these questions then click on the button marked Click on this button below to see the correct answer to see whether you are correct.

(a) Which numbers are in the union of A and B?

(b) Which numbers are in the intersection of A and B?

 

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on Click on this button to see the correct answer to see the answer.

When filling in the venn diagrams, separate the numbers in each section with commas :
The (a), (b), (c) and (d) are only in the diagram to help you when you check the answers.

Question 1
Complete the Venn diagram using the information on the right.
All the whole numbers from 1 to 10 are to be included.

Set A = { 1 , 4 , 5 , 7 , 8 }
Set B = { 2 , 6 , 8 , 10 }

Complete the sections in the Venn diagram, then use the four buttons below to check your answers.
(a)
(b)
(c)
(d)

(e) What is the intersection of A and B?
{}

Question 2
Complete the Venn diagram using the information on the right.
All the whole numbers from 1 to 10 are to be included.

Set A contains all the odd numbers in this set.
Set B contains all the numbers greater than 4.

Complete the sections in the Venn diagram, then use the four buttons below to check your answers.
(a)
(b)
(c)
(d)

(e) What is the union of A and B?
{}

Question 3
The whole numbers from 1 to 12 are included in the Venn diagram below.
(a) List set B.
{}

(b) List set A.
{}

(c) Which set contains all the even numbers?

(d) Which set contains only the multiples of 4?

Question 4
The whole numbers from 1 to 20 are included in the Venn diagram below.
(a) List set E.
{}

(b) List set S.
{}

(c) Describe set S.

(d) Describe set E.

(e) What is the intersection of E and S?

Question 5
Complete the Venn diagram using the information on the right.
The numbered shapes below are to be sorted into two sets, R and Q.
Set R contains shapes with a right-angle (90).
Set Q contains shapes with four sides.

Complete the Venn diagram, then check your answers.
(a)
(b)
(c)
(d)


You have now completed Unit 1 Section 3
Your overall score for this section is
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Produced by A.J.Reynolds January 2001