GCSE Maths Venn Diagrams & Set Notation Notes
A Venn diagram shows how sets overlap. Set notation describes the regions, and you can read probabilities straight off the diagram.
Key concepts
- Intersection (A ∩ B)
- The overlap — items that are in both sets.
- Union (A ∪ B)
- Everything in A or B or both — all shaded regions of the two sets.
- Complement (A′)
- Everything not in set A.
- Universal set (ξ)
- All the items being considered — the box around the whole diagram.
Key formulas
Probability from a Venn diagram
P(event) = items in region ÷ total items
Worked example
In a class of 30, 18 study French, 12 study German and 5 study both. How many study neither?
- 1Both = 5, so French only = 18 − 5 = 13 and German only = 12 − 5 = 7.
- 2Add the three regions: 13 + 7 + 5 = 25 study at least one language.
- 3Neither = 30 − 25 = 5.
Answer: 5 students
Common mistakes
✗ Double-counting the overlap.
✓ Fill in the intersection first, then subtract it from each set total.
✗ Confusing ∪ (union) with ∩ (intersection).
✓ ∩ is 'and' (the overlap); ∪ is 'or' (everything in either set).
✗ Forgetting the 'neither' region outside the circles.
✓ The regions must add up to the total in the universal set.
Quick check
Try these, then reveal the answers.
What does A ∩ B mean?Reveal answer
The items in both A and B.
What does A′ mean?Reveal answer
Everything not in A.
If 3 of 20 are in the overlap, P(both)?Reveal answer
3/20
Exam tips
- Always fill in the intersection region first, then work outwards.
- Check every region adds up to the total before finding probabilities.
- Learn the symbols: ∩ intersection, ∪ union, ′ complement, ξ universal set.
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Frequently asked questions
What is the difference between union and intersection?+
Intersection (∩) is what is common to both sets; union (∪) is everything in either set.
How do I find a probability from a Venn diagram?+
Divide the number of items in the relevant region by the total number of items.
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