Set Theory: Venn Diagrams

We can also represent sets using Venn diagrams. In a Venn diagram, the sets are represented by shapes; usually circles or ovals. The elements of a set are labelled within the circle.

Example:

Given the set P is the set of even numbers between 15 and 25. Draw and label a Venn diagram to represent the set P and indicate all the elements of set P in the Venn diagram.

Solution:

List out the elements of P.

P = {16, 18, 20, 22, 24} ← ‘between’ does not include 15 and 25

Draw a circle or oval. Label it P . Put the elements in P.

Example:

Draw and label a Venn diagram to represent the set

R = {Monday, Tuesday, Wednesday}.

Solution:

Draw a circle or oval. Label it R . Put the elements in R.

Example:
Given the set Q = {x : 2x – 3 < 11, x is a positive integer }. Draw and label a Venn diagram to represent the set Q.

Solution:
Since an equation is given, we need to first solve for x.
2x – 3 < 11 ⇒ 2x < 14 ⇒ x < 7

So, Q = {1, 2, 3, 4, 5, 6}

Draw a circle or oval. Label it Q .

Put the elements in Q.

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