IGCSE Maths Sets & Venn Diagrams Notes
Sets are collections of objects. IGCSE tests set notation and Venn diagrams, including union, intersection, complement and probability from a Venn diagram.
Key concepts
- Union (∪) & intersection (∩)
- Union is 'in either set'; intersection is 'in both sets'.
- Complement (A′)
- Everything in the universal set that is not in A.
- Element & subset
- ∈ means 'is a member of'; ⊂ means 'is a subset of'.
Key formulas
Elements count
n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
Worked example
In a class, n(A) = 12, n(B) = 15, n(A ∩ B) = 5. Find n(A ∪ B).
- 1Use n(A ∪ B) = n(A) + n(B) − n(A ∩ B).
- 2Substitute: 12 + 15 − 5.
- 3Calculate the total.
Answer: 22
Common mistakes
✗ Double-counting the intersection.
✓ Subtract n(A ∩ B) once when combining set totals.
✗ Confusing ∪ and ∩ symbols.
✓ ∪ (union) = either; ∩ (intersection) = both.
✗ Forgetting the universal set for complements.
✓ A′ is everything outside A within the universal set.
Quick check
Try these, then reveal the answers.
What does A ∩ B mean?Reveal answer
Elements in both A and B
What does A′ mean?Reveal answer
Everything not in A
n(A)=8, n(B)=6, n(A∩B)=2. n(A∪B)?Reveal answer
12
Exam tips
- Fill the intersection of a Venn diagram first, then work outwards.
- Learn the symbols ∪, ∩, ′, ∈ and ⊂ precisely.
- For probability, count from the Venn diagram over the total.
Related practice
Practise this topic
Exam-style questions with instant Gradion feedback.
Flashcards
Quick-fire recall to lock in the key facts.
Worksheets
Printable practice you can work through offline.
Past papers
Full papers with examiner-grade marking.
Gradion
Ask for a step-by-step explanation any time.
All Mathematics
Every Mathematics topic across every exam board.
Related topics
Frequently asked questions
What is the difference between union and intersection?+
Union (∪) includes elements in either set; intersection (∩) includes only elements in both.
How do I use a Venn diagram for probability?+
Count the elements in the region you need and divide by the total number in the universal set.
Create a free account to practise sets & venn diagrams with Gradion feedback
Try 5 questions now, get instant examiner-grade marking and ask the Gradion to explain anything. Free during our early launch period — no credit card required.