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 around this, we use **set notation.**

**What is a set?**

A set is just a list of pieces of information. They might be given as numbers, conditions, non-numerical 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**

Sets are frequently given as conditions such as B = {multiples of 4}.

Because these are infinitely 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}

Set A = {Factors of 50}

Set B = { Multiples of 2}

This means that A is the factors of 50 up to 20.

So set A = {1,2,5,10}

and B is multiples of 2, but only up to 20.

So set B = {2,4,6,8,10,12,14,16,18,20}

**Putting this info into a Venn diagram**

All Venn diagrams look something like this:

All we have to be able to do is find out which numbers go in which sections.

It's easiest to find B first, as these are the numbers that are in **both sets.**

**B = 2, 10**

A is the ones in set A that aren't already in the middle:

**A = 1,5**

C is the numbers that are in set B that aren't already in the middle:

**C = 4,6,8,12,14,16,18,20**

D is all the numbers in the universal set that we haven't yet seen:

**D = 3,7,9,11,13,15,17,19**

This should give the Venn diagram:

**What other notation do we need?**

There are a few other 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.

On the Venn diagram, this is illustrated by:

**Union:**

This would be written as **A∪B**

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

On the Venn diagram, this is illustrated by:

**Not:**

This would be written as **A'**

This means all the values that are **not**** **in A.

On the Venn diagram, this is illustrated by:

**Example:**

ε = {Numbers from 1 - 20}

Set A = { Factors of 50}

Set B = {Multiples of 2}

**Find the numbers that satisfy:**

**A∩B**

These are the numbers that satisfy **both** sets A and B and that are less than 21.

The only numbers that are less than 21 as well as being both a factor of 50 and a multiple of 2 are** 2 and 10**

**So, A∩B = 2 and 10**

**A ∪B**

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, 4, 5, 6, 8, 10, 12, 14, 16, 18, 20

**A'**

Not A means all the numbers under 21 that aren't in set A.

This means the following numbers: 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

Now let's move on to some questions.