Venn diagrams and sets are among the most searched IGCSE maths topics because they test logic and notation as well as number. You need to use set notation (∪, ∩, complement, ∈), shade the correct region for an expression, and solve problems using given numbers in regions.

Set Notation You Need

• Union (A \cup B) – In A or B or both.
• Intersection (A \cap B) – In both A and B.
• Complement (A’) – Not in A (within the universal set).
• Elements (x \in A) – x is in set A.
• Number of elements (n(A)) – Number in set A.

Shading and Problem-Solving

• Shading: For an expression like (A’ \cap B), shade only the part that is in B but not in A.
• Numbers in regions: Use “only A”, “only B”, “A and B”, “neither” (or similar) and fill in from totals and given facts.
• Algebra: Sometimes you form equations from overlapping regions (e.g. (n(A \cup B) = n(A) + n(B) - n(A \cap B))).

Practise shading and filling in numbers with past paper questions so you are confident in exams.

Worked Example and Common Mistakes

Example: Shade A’ ∩ B. Shade only the region that is in B but not in A (the part of B outside the overlap). For “how many in A ∪ B?”, use n(A) + n(B) − n(A ∩ B) or fill in the diagram. Common mistakes: Shading the wrong region (read the expression carefully: A’ ∩ B is not the same as A ∩ B’); wrong set notation (∪ = or both, ∩ = and only); arithmetic errors when filling in numbers from totals. Check that numbers in regions add up to the total given.

Tutopiya Resources and Free Trial

Tutopiya’s IGCSE Maths tutors can help you master Venn diagrams and sets with clear notation and exam-style problems.

Book a free trial with an IGCSE Maths tutor or explore Tutopiya’s learning portal for free resources and sets practice.