18 min read

Venn Diagrams

A Venn diagram uses overlapping circles to show how sets relate to each other.

Reading a Venn Diagram

A Venn diagram draws each set as a circle inside a rectangle (the universal set U). Where circles overlap shows elements that belong to both sets. Elements inside the rectangle but outside every circle belong to neither set.

Change a value and watch:

6 is in both circles because it is both even and a multiple of 3 . Try the buttons to highlight different regions.

Set A = {2, 4, 6, 8} and Set B = {3, 6, 9}, drawn from the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9}.

Example 1 — placing elements

Let A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, with U = {1, 2, 3, 4, 5, 6}. 1 Elements in both A and B go in the overlap: 3 and 4 . 2 Elements only in A go in the left part of A's circle: 1 and 2 . 3 Elements only in B go in the right part of B's circle: 5 and 6 . 4 There are no elements left outside both circles, since U only has 1 to 6 .

Practice

In a Venn diagram for A and B, where would an element that is in neither set be drawn?

Reading a Venn Diagram

A Venn diagram draws each set as a circle inside a rectangle (the universal set U). Where circles overlap shows elements that belong to both sets. Elements inside the rectangle but outside every circle belong to neither set.

Change a value and watch:

6 is in both circles because it is both even and a multiple of 3 . Try the buttons to highlight different regions.

Set A = {2, 4, 6, 8} and Set B = {3, 6, 9}, drawn from the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9}.

Example 1 — placing elements

Let A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, with U = {1, 2, 3, 4, 5, 6}. 1 Elements in both A and B go in the overlap: 3 and 4 . 2 Elements only in A go in the left part of A's circle: 1 and 2 . 3 Elements only in B go in the right part of B's circle: 5 and 6 . 4 There are no elements left outside both circles, since U only has 1 to 6 .

Practice

In a Venn diagram for A and B, where would an element that is in neither set be drawn?