# What Is A Venn Diagram? Mathematics for WASSCE and BECE candidates

### What Is A Venn Diagram? Mathematics for WASSCE and BECE candidates

A Venn Diagram is a pictorial representation of the relationships between sets.

We can 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 labeled within the circle.

The following diagrams show the set operations and Venn Diagrams for Complement of a Set, Disjoint Sets, Subsets, Intersection and Union of Sets. Scroll down the page for more examples and solutions.

The set of all elements being considered is called the **Universal Set (U)** and is represented by a rectangle.

- The
**complement of A, A’**, is the set of elements in U but not in A. A’ ={*x*|*x*∈ U and*x*∉ A} - Sets A and B are
**disjoint sets**if they do not share any common elements. - B is a
**proper subset**of A. This means B is a subset of A, but B ≠ A. - The
**intersection of A and B**is the set of elements in both set A and set B. A ∩ B = {*x*|*x*∈ A and*x*∈ B} - The
**union of A and B**is the set of elements in set A or set B. A ∪ B = {*x*|*x*∈ A or*x*∈ B} - A ∩ ∅ = ∅
- A ∪ ∅ = A

### Set Operations And Venn Diagrams

Example:

1. Create a Venn Diagram to show the relationship among the sets.

U is the set of whole numbers from 1 to 15.

A is the set of multiples of 3.

B is the set of primes.

C is the set of odd numbers.

2. Given the following Venn Diagram determine each of the following set.

a) A ∩ B

b) A ∪ B

c) (A ∪ B)’

d) A’ ∩ B

e) A ∪ B’

READ: **25 Basic Sets and Venn Diagram Tips and Formulae for BECE and WASSCE Exams**

### Venn Diagram Examples

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* : 2*x* – 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*.

2*x* – 3 < 11 ⇒ 2*x* < 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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