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# Venn Diagrams (Foundation)
- URL: https://www.esheets.io/venn-diagrams-foundation/
- Published: 2026-08-20T17:32:27.000Z
- Updated: 2026-08-20T17:32:27.000Z
- Author: Richard Linnington
- Tags: Maths, Probability

This worksheet provides practice on foundation-tier Venn diagrams. You’ll learn how to interpret Venn diagrams, use set notation, and find straightforward probabilities.

Venn diagrams are an excellent way to sort information visually. They help you quickly see how many people or items belong to different categories, and importantly, how many belong to both categories at once (the overlap).

By working through these questions, you’ll become confident reading frequency diagrams and using notation like $A \\cap B$ and $A \\cup B$ correctly. [Jump to the questions](#practise-now)

## Practise now

Worksheet preview and key skills 

### Worksheet preview

In this worksheet, you will complete Venn diagrams from written descriptions and answer probability questions based on the frequencies.

You will also practise matching set notation to the correct regions on the diagram.

#### What you’ll practise

- Listing the members of sets from a completed Venn diagram.
- Understanding basic set notation including intersection ($\\cap$), union ($\\cup$) and complement ($'$).
- Sorting numbers into the correct regions using simple rules.
- Completing frequency diagrams using totals and 'neither' information.
- Calculating simple probabilities from a completed Venn diagram.

Use the interactive worksheet below, or read the [Topic guide](#topic-guide) for the method and worked example.

## Venn diagrams (Foundation)

Complete the questions below. For lists of numbers, you can write them in any order separated by commas.

## Topic guide

A Venn diagram uses overlapping circles to show relationships between different sets of items. The large rectangle surrounding the circles is the **universal set** (often labelled with $\\xi$), which contains everything being considered in the problem.

### Key set notation

You need to know these three important symbols:

- **Intersection ($A \\cap B$):** This is the overlap. It contains items that are in *both* set A and set B.
- **Union ($A \\cup B$):** This contains all items that are in set A, *or* set B, *or* both. It covers everything inside the two circles.
- **Complement ($A'$):** This means 'not A'. It contains everything in the universal set that is *outside* of circle A.

### Completing frequency Venn diagrams

When completing a Venn diagram from survey data, always start with the overlap (the people who do both) if possible, and work outwards.

**Example:** In a class of 30 students, 18 play football, 15 play tennis, and 6 play both. Draw a Venn diagram to show this.

1. **Overlap:** Put the 6 students who play both in the middle section.
2. **Football only:** Since 18 play football in total, and 6 are already in the overlap, $18 - 6 = 12$ play *only* football.
3. **Tennis only:** Since 15 play tennis in total, and 6 are in the overlap, $15 - 6 = 9$ play *only* tennis.
4. **Neither:** The total number of students in the circles so far is $12 + 6 + 9 = 27$. Since there are 30 students in the class, $30 - 27 = 3$ play neither. Put the 3 outside the circles.

### Finding probabilities

Once your Venn diagram is complete, you can find probabilities by dividing the number of successful outcomes by the total number in the universal set.

In our example above, the probability that a randomly chosen student plays only football is $\\frac{12}{30}$, which simplifies to $\\frac{2}{5}$.