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Sets for OCR GCSE Maths

Sets

This page covers the following topics:

1. Set notation
2. Combinations of sets
3. Tables
4. Grids
5. Venn diagrams

Set notation is used to list numbers and outcomes using curly brackets {}. The universal set, denoted as ฮพ, includes all the relevant values. Given a set A and an element of it a, a โˆˆ A states that a is an element of A.

Set notation

If every element in a set A is also an element of set B, set A is said to be a subset of set B, A โŠ† B. Given two sets A and B, AโˆฉB represents the intersection between the two sets, AโˆชB represents the union between the two sets and A' represents everything not in set A.

Combinations of sets

Data collected from an experiment can be presented in a two-way table. The table will show the frequency of each group represented on it.

Tables

Grids can be used to represent two or more sets. Sample space diagrams are grids which record all the possible outcomes of two events. These diagrams can then be used to calculate probabilities.

Grids

Venn diagrams are a diagram that groups different sets. The box the venn diagrams are placed in represents the universal set. The circles inside the box represent the different sets. Circles within each other represent subsets and overlapping circles represent the intersection between sets. The numbers on Venn diagrams can either represent the number of values in a set or the actual values. The following formula can be used to find the missing values in a Venn diagram: P(AโˆชB) = P(A) + P(B) โˆ’ P(AโˆฉB).

Venn diagrams

1

Set U is {10, 11, 12, 13, 14, 15} and set V is {5, 10, 15}. State UโˆฉV.

UโˆฉV = {10, 15}.

Set U is {10, 11, 12, 13, 14, 15} and set V is {5, 10, 15}. State UโˆฉV.

2

Two dice are rolled and the sum of the rolls is recorded. Draw a sample space diagram to represent all the possible outcomes.

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Two dice are rolled and the sum of the rolls is recorded. Draw a sample space diagram to represent all the possible outcomes.

3

Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and B = {2, 4, 6, 8, 10, 12, 14, 16}. Draw a Venn diagram to represent this data.

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Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and B = {2, 4, 6, 8, 10, 12, 14, 16}. Draw a Venn diagram to represent this data.

4

A set X is defined as {2, 3, 4, 5, 6, 7}. State whether 8 โˆˆ X.

8 is not an element of the set, therefore 8 โˆˆ X is false.

A set X is defined as {2, 3, 4, 5, 6, 7}. State whether 8 โˆˆ X.

5

How can subsets be represented in Venn diagrams?

A circle drawn within a circle shows that the inner circle is a subset of the outer circle.

How can subsets be represented in Venn diagrams?

End of page

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