Venn diagrams - WJEC

Venn diagrams are a useful tool in the world of statistics. Once you have got to grips with these, you will be able to arrange all sorts of groups and sets.

What are Venn diagrams?

A Venn diagram is a way of grouping different items. These groups are known as sets.

We have a set of golf clubs or a set of dishes – these are just groups of those items.

We write a set using a special type of brackets. You could have a set of friends, eg {tom, leanne, alison, nia, anna, suzanne, lucy, marie}. Notice you don’t use capitals within the brackets.

A Venn diagram begins with a box called our universal set, which is denoted by the symbol ε (epsilon).

The universal set contains everything we are interested in at that particular time. There’ll be circles inside the box which we use to group the items within the universal set. Items in the circles form different subsets.

A Venn diagram with two sets labelled Set A and Set B. Set A contains 8 numbers and Set B contains 9 numbers. The two sets overlap in the middle to form a subset containing 4 numbers

Subsets

Set A is the numbers in the circle labelled Set A.

Set A = {1, 5, 6, 7, 8, 9, 10, 12}

Set B is the numbers in the circle labelled Set B.

Set B = {2, 3, 4, 6, 7, 9, 11, 12, 13}

These are the subsets of the universal.

Intersection

The intersection is where we have items from Set A and Set B, these can be found in the section that overlaps.

We write it as {A}\cap{B}. In the example above {A}\cap{B} = {6, 7, 9, 12}.

Union

The union of a Venn diagram is the numbers that are in either Set A or Set B.

The union of the above example is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 as it’s the numbers that appear in either of the circles.

We write it as {A}\cup{B} = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}

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