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Set notation is used in mathematics to essentially list numbers, objects or outcomes.

Set notation uses curly brackets { } which are sometimes referred to as braces. Objects placed within the brackets are called the elements of a set, and do not have to be in any specific order. Sets are named using capital letters with some sets having a predefined name.

N is the set of counting or natural numbers:

N = {1, 2, 3, 4, 5...}

Z is the set of integers:

Z = {...-3, -2, -1, 0, 1, 2, 3...}

We can define our own sets and choose any letter we want to represent them:

• D = {80, 90, 100, 200}
• E = {blue, green, red}
• F = {carpet, chair, desk}

We can also use notation to create our sets:

Z = {x ∶ x is a factor of 18}

This is read as 'Z is a set of the factors of 18'.

This set could also be defined by us saying:

Z = {1, 2, 3, 6, 9, 18}

When we have two or more sets, we can look at how they are the same or how they differ in lots of different ways.

For example, if set A completely fits into set B, we can say that A ⊂ B.

If A = {1, 3, 5} and B = {1, 3, 5, 7, 9}

Then A ⊂ B

We say that 'A is a subset of B'.

If this was not true, we would say A ⊄ B meaning A is not a subset of B.

Using A = {1, 2, 3, 4, 5} and B = {2, 4, 6, 8, 10} we can find the intersection of A and B which is written as A ∩ B. This means things that are in set A and also in set B.

In the example above, A ∩ B = {2, 4}

We can also find the union of A and B which is written as A ∪ B. This means things that are in either set A or set B.

In the above example A ∪ B = {1, 2, 3, 4, 5, 6, 8, 10}

Finally, if we want to list the elements not in Set A, we can use the notation A’ called the complement of A. In the example above, A’ = {6, 7, 8, 9, 10...}