P6 Mathematics - Term I

Topic 1: Sets

Lesson 3: Venn Diagrams

Duration: 45 minutes

Today's Learning Objectives for Venn Diagrams

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

• Draw Venn diagrams to represent sets
• Display information on Venn diagrams for 2 sets
• Read and interpret information from Venn diagrams
• Show union and intersection on Venn diagrams
• Represent universal sets, subsets, complements visually

Quick Review Before We Start Drawing

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

The Basic Structure of a Venn Diagram

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

Drawing Your First Venn Diagram

Example:

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

Steps:

1. Draw a rectangle for U, circle for A
2. Write elements of A inside the circle
3. Write other elements outside the circle
4. Label U and A

Practice: Draw This 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 Can Overlap

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: Two Sets That Overlap

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 Combines Everything (A ∪ B)

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

Symbol: ∪

A ∪ B = Combine everything from both sets

Finding a Union in Practice

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}

Intersection Keeps Only What's Shared (A ∩ B)

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

Symbol: ∩

A ∩ B = Only the shared elements

Finding an Intersection in Practice

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

Comparing Union and Intersection Side by Side

Remember: Union = everything, Intersection = only shared

Practice: Read This 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? In B only?
2. What is in both A and B?
3. What is in neither set?

Checking Your Venn Diagram 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}

More Practice with Union and Intersection

Using the same sets:

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

Find:

• A ∪ B = ?
• A ∩ B = ?

Checking the Union and Intersection

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

A ∩ B = {3, 4}
(Only common elements)

A Real-Life Venn Diagram Example

Example: Learners in class

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

Venn diagram shows: red only, shoes only, both, or neither

Steps for Drawing Any Venn Diagram

1. Draw rectangle for U, circles for A and B
2. Start with the intersection (overlap)
3. Put "A only" elements in A (not overlap)
4. Put "B only" elements in B (not overlap)
5. Put remaining elements outside circles
6. Label everything clearly

Practice Problem: Build Your Own Diagram

U = {10, 11, ..., 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!

Solving the Venn Diagram Practice Problem

Intersection (A ∩ B): {16, 18, 20}

A only: {10, 12, 14}

B only: {15, 17, 19}

Neither: {11, 13}

Summary: Venn Diagrams and Set Operations

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

Tonight's Homework on Venn Diagrams

1. Draw a Venn diagram for:

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

2. Find: A ∩ B, A ∪ B, A only, B only

Expected time: 25-30 minutes

Preview: Venn Diagrams and Probability

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!

Lesson Credits and Curriculum Source

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/