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Understand Set Notation

In this worksheet, students practise using simple set notation.

'Understand Set Notation' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Probability

Curriculum subtopic:   Probability, Combined Events and Probability Diagrams

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

When you are looking at data that has been sorted, describing which piece of information you are looking for can be quite difficult.

To get round this we use set notation.

 

What is a Set?

A set is just a list of pieces of information. They could be given as numbers, conditions, nonnumerical data. Just about anything.

Sets are always written inside a curly bracket, for example A = {1,2,3,4,5,6} or B = {multiples of 4}

 

The universal set:

When you look at a set question, sets are frequently given as conditions such as B = {multiples of 4}.

Because these are infinitly long, we need to limit this using the universal set.

This is just the set of numbers that the question is limited to, we use the symbol ε

 

For example:

ε = {Numbers from 1 - 20}

A = { Multiples of 3}

B = {Factors of 50}

This means A is the multiples of 3 up to 20

So A = {3,6,9,12,15,18}

We also have B being the factors of 50, but only up to 20.

So B = {1,2,5,10}

 

What other Notation do we need?

There are a number of set notations that you need to know for GCSE Maths.

INTERSECTION: This would be written as AB

This means all the values that are in A and B

UNION: This would be written as AB

This means all the values that are in A or B

NOT: This would be written as A'

This means all the values that are not in A

 

Example:

ε = {Numbers from 1 - 20}

A = { Multiples of 2}

B = {Factors of 50}

Find the numbers that satisfy;

A∩B

These are the numbers that satisfy both set A and B and that are less than 20

The only numbers that are both a factor of 50, a multiple of 2 and less than 20 are 2 and 10

AB

This means we want all the numbers that are either a multiple of 2 or a factor of 50 (and still under the limit of 21)

This gives us the numbers 1, 2, 3, 4, 5, 6, 8, 9. 10, 12, 14, 16, 18, 20

A'

Not A means all the numbers that aren't in set A.

This means the following numbers 1, 3, 5, 7, 9, 11, 13, 15, 17, 19

 

 

ε = {Numbers from 1 - 20}

A = {Even numbers}

B = {Factors of 20}

 

If I select a number at ransom, what is the probability it will be in set A?

 

Give your answer as a simplified fraction in the form a/b

ε = {Numbers from 1 - 20}

A = {Even numbers}

B = {Factors of 20}

 

For each of the numbers from 1 - 20, select if it is in either Set A, Set B, Both A and B or netiher set.

 Set ASet BBoth setsNeither set
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

ε = {Numbers from 1 - 20}

A = {Even numbers}

B = {Factors of 20}

 

If I select a number at random, what is P(A∩B)

 

Give your answer as a simplified fraction in the form a/b

1/5

3/5

ε = {Numbers from 1 - 20}

A = {Even numbers}

B = {Factors of 20}

 

If I select a number at random, what is P(B')

 

Give your answer as a simplified fraction in the form a/b

3/10

7/10

ε = {Numbers from 1 - 20}

A = {Even numbers}

B = {Factors of 20}

 

If I select a number at random, what is P(A∪B)

 

Give your answer as a simplified fraction in the form a/b

ε = {Numbers from 1 - 15}

A = {Mulitples of 3}

B = {Factors of 12}

 

For each of the numbers from 1 - 20, select if it is in either Set A, Set B, Both A and B or netiher set.

 Set ASet BBoth setsNeither set
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

ε = {Numbers from 1 - 15}

A = {Mulitples of 3}

B = {Factors of 12}

 

If I select a number at random, what is P(A)

 

Give your answer as a simplified fraction of the form a/b

ε = {Numbers from 1 - 15}

A = {Mulitples of 3}

B = {Factors of 12}

 

If I select a number at random, what is P(A∩B)

 

Give your answer as a simplified fraction of the form a/b

1/5

1/3

ε = {Numbers from 1 - 15}

A = {Mulitples of 3}

B = {Factors of 12}

 

If I select a number at random, what is P(B')

 

Give your answer as a simplified fraction of the form a/b

2/3

1/3

ε = {Numbers from 1 - 15}

A = {Mulitples of 3}

B = {Factors of 12}

 

If I select a number at random, what is P(A∪B)

 

Give your answer as a fraction of the form a/b

  • Question 1

ε = {Numbers from 1 - 20}

A = {Even numbers}

B = {Factors of 20}

 

If I select a number at ransom, what is the probability it will be in set A?

 

Give your answer as a simplified fraction in the form a/b

CORRECT ANSWER
1/2
EDDIE SAYS
The easist way to do this is to list the numbers Set A = {Even numbers} = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} We have 10 numbers out of the 20 in total
  • Question 2

ε = {Numbers from 1 - 20}

A = {Even numbers}

B = {Factors of 20}

 

For each of the numbers from 1 - 20, select if it is in either Set A, Set B, Both A and B or netiher set.

CORRECT ANSWER
 Set ASet BBoth setsNeither set
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
EDDIE SAYS
The first thing we need to do here is state what numbers the sets represent. ε = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20} A = {2,4,6,8,10,12,14,16,18,20} B = {1,2,4,5,10,20} From this, we can see the ones that are in both initially, in A next then in B. Once we have this, all the ones we haven't used are in neither set.
  • Question 3

ε = {Numbers from 1 - 20}

A = {Even numbers}

B = {Factors of 20}

 

If I select a number at random, what is P(A∩B)

 

Give your answer as a simplified fraction in the form a/b

CORRECT ANSWER
1/5
EDDIE SAYS
A∩B is A AND B Set A = {Even numbers} = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} Set B = {Factors of 20} = {1,2,4,5,10,20} From this, we can see we have 4 numbers that appear in both, this gives a probability of 4/20 which cancels down to...
  • Question 4

ε = {Numbers from 1 - 20}

A = {Even numbers}

B = {Factors of 20}

 

If I select a number at random, what is P(B')

 

Give your answer as a simplified fraction in the form a/b

CORRECT ANSWER
3/10
EDDIE SAYS
B' is not in B Set B = {Factors of 20} = {1,2,4,5,10,20} From this, we can see we have 6 numbers that appear in B, so we have 14 that don't. This gives a probability of 14/20 which cancels down to...
  • Question 5

ε = {Numbers from 1 - 20}

A = {Even numbers}

B = {Factors of 20}

 

If I select a number at random, what is P(A∪B)

 

Give your answer as a simplified fraction in the form a/b

CORRECT ANSWER
3/10
EDDIE SAYS
A∪B is A OR B Set A = {Even numbers} = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} Set B = {Factors of 20} = {1,2,4,5,10,20} From this, we can see we have 12 numbers that appear in both, this gives a probability of 12/20 which cancels down to...
  • Question 6

ε = {Numbers from 1 - 15}

A = {Mulitples of 3}

B = {Factors of 12}

 

For each of the numbers from 1 - 20, select if it is in either Set A, Set B, Both A and B or netiher set.

CORRECT ANSWER
 Set ASet BBoth setsNeither set
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
EDDIE SAYS
The first thing we need to do here is state what numbers the sets represent. ε = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15} A = {3,6,9,12,15 B = {1,2,3,4,6,12} From this, we can see the ones that are in both initially, in A next then in B. Once we have this, all the ones we haven't used are in neither set.
  • Question 7

ε = {Numbers from 1 - 15}

A = {Mulitples of 3}

B = {Factors of 12}

 

If I select a number at random, what is P(A)

 

Give your answer as a simplified fraction of the form a/b

CORRECT ANSWER
EDDIE SAYS
A = {3,6,9,12,15} B = {1,2,3,4,6,12} We have 5 numbers in set A and 15 numbers in total.
  • Question 8

ε = {Numbers from 1 - 15}

A = {Mulitples of 3}

B = {Factors of 12}

 

If I select a number at random, what is P(A∩B)

 

Give your answer as a simplified fraction of the form a/b

CORRECT ANSWER
1/5
EDDIE SAYS
A = {3,6,9,12,15} B = {1,2,3,4,6,12} We have 3 numbers in set A and B and 15 numbers in total.
  • Question 9

ε = {Numbers from 1 - 15}

A = {Mulitples of 3}

B = {Factors of 12}

 

If I select a number at random, what is P(B')

 

Give your answer as a simplified fraction of the form a/b

CORRECT ANSWER
1/3
EDDIE SAYS
A = {3,6,9,12,15} B = {1,2,3,4,6,12} We have 5 numbers in set B so we have 10 that aren't. 10 out of the 15 numbers we have cancels down to...
  • Question 10

ε = {Numbers from 1 - 15}

A = {Mulitples of 3}

B = {Factors of 12}

 

If I select a number at random, what is P(A∪B)

 

Give your answer as a fraction of the form a/b

CORRECT ANSWER
8/15
EDDIE SAYS
A = {3,6,9,12,15} B = {1,2,3,4,6,12} We have 8 numbers that are in either Set A or Set B and 15 numbers in total.
---- OR ----

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