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 simply a list of pieces of information. It could be given as numbers, conditions, non-numerical data or 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 one of these types of question, sets are frequently given as** conditions**,

such as **B = {multiples of 4}**.

Because this is infinitely long, we need to limit it 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 tha**t 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 **A∩B**

This means all the values that are in A **and** B.

**Union:** This would be written as **A∪B**

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 20 or less.

The only numbers that are both a factor of 50 and a multiple of 2, as well as being 20 or less are **2 and 10.**

**A ∪B**

This means we want all the numbers that are** either** a multiple of 2 **or **a factor of 50 (but 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

There's a lot to remember here, so let's test it out in some questions.