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.

Venn diagrams are very useful constructs made of two or more circles that sometimes overlap. Venn diagrams frequently appear in different areas of mathematics but are most common when dealing with sets and probability.

Look at this Venn diagram:

It shows Set A = {1, 5, 6, 7, 8, 9, 10, 12} and Set B = {2, 3, 4, 6, 7, 9, 11, 12, 13}

If we look at the overlapping section of the Venn diagram, this represents A ∩ B = {6, 7, 9, 12} (The intersection of A and B). This contains the numbers that are in both Set A and Set B.

Taking the two circles in their entirety gives us A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13} (The union of A and B).

Two sets

The Venn diagram below is the graphical representation of two more sets. The sets represent information about two sisters - Leah (L) and Kelly (K) and their interests.

We could write the sets as L = {read, play netball, draw} and K = {dance, skate, listen to music}.

From the diagram, we see that there is no intersection (L ∩ K = {}) meaning that they have no interests in common.

The union of these two sets would be the set containing the interests of Leah and Kelly:

L ∪ K = {read, play netball, draw, dance, skate, listen to music}

Try answering the questions below:

Question

List the items in:

Set A

Set B

Set A = {12, 14, 15, 16, 17, 18, 20, 22}

Set B = {16, 17, 20, 21, 22, 23, 24, 25, 28}

Question

List the intersection and union of the following Venn diagram:

Intersection – A ∩ B = {3, 7, 9, 20}

Union – A ∪ B = {3, 7, 9, 10, 14, 15, 19, 20, 23, 24, 25, 26, 30}