# Unit 1 Section 4 : Set Notation

In this section we look at some mathematical notation for the ideas we learnt about sets in the last section.
 We use to denote the universal set, which is all of the items which can appear in any set. This is usually represented by the outside rectangle on the venn diagram. A B represents the intersection of sets A and B. This is all the items which appear in set A and in set B. A B represents the union of sets A and B. This is all the items which appear in set A or in set B or in both sets. ' We use ' (the apostrophe) to denote the complement of a set. A' is all the items which are not in set A. A B means that set A is a subset of set B. This means that every member of set A also appears in set B. is the empty set - a set with no items in it. For example, if A is the set of numbers which are both odd and even then A = .
Practice Questions
Work out the answer to each of these questions then click on the button marked to see whether you are correct.

 Look at the venn diagram on the left. List the items which are in the set: (a) A B (b) A' B Look at the venn diagram on the left. List the items which are in the set: (a) B' (b) (A B) C' Look at the venn diagrams on the left. Use set notation to describe: (a) the area shaded in green (b) the area shaded in red Look at the venn diagrams on the left. Use set notation to describe: (a) the area shaded in blue (b) the area shaded in purple Look at the venn diagram on the left. State whether each of the following statements are TRUE or FALSE: (a) R = { f , i , h } (b) P Q (c) P Q = P (d) P R = (e) (Q R)' = { k , m }

## Exercises

Work out the answers to the questions below and fill in the boxes. Click on the 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 to see the answer.

When filling in the sets or venn diagrams below, separate the numbers in each section with commas: {}

Question 1

The venn diagram below illustrates set A and B:

Find:
 (a) A B {} (b) (A B)' {} (c) A B {} (d) A' {} (e) B' {} (f)  A' B' {} (g) A' B {}

Question 2

= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {2, 4, 6, 8}
B = {3, 6, 9}

Find:
 (a) A B {} (b) A B {} (c) A' {} (d) B' {} (e) A' B' {} (f)  A' B' {}

Question 3

 (a)          (b)          (c)         (d)         (e)                 (f)       (g)          (h)

The sets in the venn diagram are as follows:

= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
A = {1, 2, 3, 4, 5, 6}
B = {2, 4, 6, 8, 10, 12, 14}
C = {3, 6, 9, 12, 15}

Fill in the gaps in the venn diagram and then
check each section using the buttons below:
 (a) (b) (c) (d) (e) (f) (g) (h)

Now find the contents of these sets using the diagram:
 (i) A B {} (j) A C {} (k) B C {} (l) A B {} (m) A C {} (n) C' {} (o) A C' {} (p) A B C {}

Question 4

Look at these venn diagrams.

Select the diagram where the shaded area matches the set notation below:
 (a) P Q Diagram A Diagram B Diagram C Diagram D Diagram E Diagram F (b) Q Diagram A Diagram B Diagram C Diagram D Diagram E Diagram F (c) P Q Diagram A Diagram B Diagram C Diagram D Diagram E Diagram F (d) Q P' Diagram A Diagram B Diagram C Diagram D Diagram E Diagram F (e) (P Q)' Diagram A Diagram B Diagram C Diagram D Diagram E Diagram F (f)  Q' Diagram A Diagram B Diagram C Diagram D Diagram E Diagram F (g) P' Q' Diagram A Diagram B Diagram C Diagram D Diagram E Diagram F

Question 5

Look at these venn diagrams.

Select the diagram where the shaded area matches the set notation below:
 (a) Q R Diagram A Diagram B Diagram C Diagram D Diagram E Diagram F (b) P Q R Diagram A Diagram B Diagram C Diagram D Diagram E Diagram F (c) Q R P' Diagram A Diagram B Diagram C Diagram D Diagram E Diagram F (d) P Q Diagram A Diagram B Diagram C Diagram D Diagram E Diagram F (e) P' R' Q Diagram A Diagram B Diagram C Diagram D Diagram E Diagram F (f) (P Q) R' Diagram A Diagram B Diagram C Diagram D Diagram E Diagram F (g) Q (P R)' Diagram A Diagram B Diagram C Diagram D Diagram E Diagram F

Question 6

The venn diagram below illustrates 3 sets A, B and C:

Decide if each of the following statements is true or false:
 (a) A B True False (b) B C True False (c) A B = A True False (d) A B = C True False (e) A C = True False (f)  B C = True False (g) B A = B True False

Question 7

= {a, b, c, d, e, f, g, h}
A = {a, c, e}
B = {b, d, g, h}
C = {a, c, e, f}

Say whether each of the following statements is true or false:
 (a) B C = True False (b) C A True False (c) B C = True False (d) A C = {a, c, e, f} True False (e) (A C)' = {b, d, f, g, h} True False (f)  B True False (g) A B' = C True False

You have now completed Unit 1 Section 4
 Your overall score for this section is Correct Answers You answered questions correctly out of the questions in this section. Incorrect Answers There were questions where you used the Tell Me button. There were questions with wrong answers. There were questions you didn't attempt.
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