P6 Mathematics - Term I

Topic 1: Sets

Lesson 3: Venn Diagrams

Duration: 45 minutes

Learning Objectives

By the end of this lesson, you will be able to:

• Draw Venn diagrams to represent sets
• Display information on Venn diagrams for up to 2 sets
• Read and interpret information from Venn diagrams
• Show union and intersection of sets using Venn diagrams
• Represent universal sets, subsets, and complement sets on Venn diagrams

Review: What We've Learned

Lesson 1: Types of sets (equal, equivalent, unequal)

Lesson 2: Universal sets, complement sets, subsets

Today: We learn to DRAW sets using Venn diagrams!

Why? Venn diagrams help us SEE set relationships visually

What is a Venn Diagram?

A Venn diagram is a visual way to show sets using:

• Rectangle = Universal set (U)
• Circles = Sets (A, B, etc.)

Named after: John Venn, a mathematician

Purpose: Makes set relationships easier to see and understand

Basic Venn Diagram Structure

• Rectangle represents U (universal set)
• Circle represents set A
• Area outside circle (but inside rectangle) = A'

Drawing a Simple Venn Diagram

Example:

U = {1, 2, 3, 4, 5, 6, 7, 8}
A = {2, 4, 6, 8}

Steps:

1. Draw a rectangle (for U)
2. Draw a circle inside (for A)
3. Write elements of A inside the circle: 2, 4, 6, 8
4. Write other elements outside circle: 1, 3, 5, 7
5. Label: U and A

Practice: Draw in Your Book

U = {a, b, c, d, e, f}
B = {a, c, e}

Draw:

1. Rectangle for U
2. Circle for B
3. Place: a, c, e inside circle
4. Place: b, d, f outside circle (but inside rectangle)

Two-Set Venn Diagrams

When we have TWO sets, circles can:

• Not overlap (disjoint sets - no common elements)
• Overlap (sets share some elements)

Today we focus on overlapping circles!

Example: Overlapping Sets

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 3, 4, 5}
B = {2, 4, 6, 8, 10}

Question: Which numbers are in BOTH A and B?

Answer: 2 and 4

These go in the overlapping part!

Union of Sets (A ∪ B)

Union means ALL elements in A OR B (or both)

Symbol: ∪

A ∪ B = Combine everything from both sets

Example: Union

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 3, 4, 5}
B = {2, 4, 6, 8, 10}

Find A ∪ B:

A ∪ B = {1, 2, 3, 4, 5, 6, 8, 10}

Count: All elements that appear in A or B or both

Intersection of Sets (A ∩ B)

Intersection means elements in BOTH A AND B (common elements)

Symbol: ∩

A ∩ B = Only the shared elements

Example: Intersection

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 3, 4, 5}
B = {2, 4, 6, 8, 10}

Find A ∩ B:

A ∩ B = {2, 4}

These are the ONLY numbers in BOTH sets

Union vs Intersection

Remember:

• Union = OR = everything
• Intersection = AND = only what's shared

Practice: Reading a Venn Diagram

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 3, 4}
B = {3, 4, 5, 6}

Questions:

1. What is in A only?
2. What is in B only?
3. What is in both A and B?
4. What is in neither A nor B?

Answers

1. A only: {1, 2}
2. B only: {5, 6}
3. Both A and B (A ∩ B): {3, 4}
4. Neither (outside both circles): {7, 8, 9, 10}

Practice: Union and Intersection

Using the same sets:

A = {1, 2, 3, 4}
B = {3, 4, 5, 6}

Find:

• A ∪ B = ?
• A ∩ B = ?

Answers

A ∪ B = {1, 2, 3, 4, 5, 6}
(All elements from both sets)

A ∩ B = {3, 4}
(Only common elements)

Real-Life Venn Diagram

Example: Learners in class

U = {all learners in class}
A = {learners wearing red}
B = {learners wearing shoes}

Venn diagram shows:

• Red only (no shoes)
• Shoes only (no red)
• Both red AND shoes (overlap)
• Neither red nor shoes (outside both circles)

Steps to Draw Venn Diagrams

1. Draw rectangle for U (universal set)
2. Draw circles for sets A and B
3. Start with intersection (overlap) - put common elements there
4. Put "A only" elements in A (not in overlap)
5. Put "B only" elements in B (not in overlap)
6. Put remaining elements outside circles (but in rectangle)
7. Label everything clearly

Practice Problem

U = {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
A = {10, 12, 14, 16, 18, 20} (even numbers)
B = {15, 16, 17, 18, 19, 20} (numbers ≥ 15)

Draw the Venn diagram in your book!

Solution

Intersection (A ∩ B): {16, 18, 20}

A only: {10, 12, 14}

B only: {15, 17, 19}

Neither: {11, 13}

Summary

Venn diagrams:

• Rectangle = Universal set (U)
• Circles = Sets (A, B)
• Overlapping part = Intersection (A ∩ B)
• Combined circles = Union (A ∪ B)

Key skill: Reading AND drawing Venn diagrams

Homework

1. Draw a Venn diagram for:

   U = {a, b, c, d, e, f, g, h, i, j}
   A = {a, b, c, d, e}
   B = {d, e, f, g}
   

2. Using your diagram, find:

   • A ∩ B
   • A ∪ B
   • Elements in A only
   • Elements in B only

Expected time: 25-30 minutes

Next Lesson Preview

Tomorrow we will learn:

• How to use Venn diagrams to calculate probabilities
• Solving probability problems with sets
• Real-life probability applications

Venn diagrams make probability easier!

Credits

Created: November 21, 2025
Based on: NCDC P6 Mathematics Curriculum - Topic 1: Sets

Source: National Curriculum Development Centre (NCDC), Uganda

Available from: https://ncdc.go.ug/