Sets and Venn diagrams for Singapore O-Level G3 Math
A set is a collection of distinct elements. A ∩ B means in both sets; A ∪ B means in either or both. A′ means outside A but inside the universal set. The notation n(A) counts elements; it is not the set itself.
What this guide covers
Set membership, subsets, complements, unions and intersections of two sets, with Venn diagrams. A complement is always relative to a stated universal set.
Syllabus reference: 2026 Mathematics 4052, N8, page 8. These are Mentora search groupings, not new official syllabus categories.
The content in this guide was also checked against 2027 G3 Mathematics K310, N8, page 8 on 2026-09-12. This is subject-content alignment, not a claim of complete syllabus coverage.
Use this guide for revision
What questions usually test
- Translate membership, subset, union, intersection and complement notation.
- Place overlap counts before exclusive regions in a two-set diagram.
- Use the stated universal set to count those in neither set or in a complement.
How to revise sets and venn diagrams
Step 1
Define the universal set
Keep the rectangle and its total in view before filling the circles.
Step 2
Fill the overlap first
Subtract the shared count before recording each exclusive region.
Step 3
Reconcile the total
Add all disjoint regions once and compare with the number given.
Worked example
Let U = {1, 2, 3, 4, 5, 6}, A = {1, 2, 3, 4} and B = {3, 4, 5}. Find A ∩ B and A ∩ B′.
A ∩ B = {3, 4}, the overlap. B′ = {1, 2, 6}; keeping only its elements also in A gives A ∩ B′ = {1, 2}, the A-only region. A ∪ B = {1, 2, 3, 4, 5}; count shared elements once.
Try three practice checks
Attempt each on paper before revealing the worked answer. These sample particular skills; they do not diagnose the whole topic or establish mastery.
Check 1
Using the example sets, find A′ and n(A ∪ B).
Show worked answer
A′ = {5, 6}. The union contains five distinct elements, so n(A ∪ B) = 5.
Check 2
In a class of 30, 18 play chess, 14 swim and 7 do both. How many do neither?
Show worked answer
The union has 18 + 14 − 7 = 25 students. Neither has 30 − 25 = 5. The disjoint regions are chess only 11, both 7, swimming only 7, neither 5; they sum to 30.
Check 3
For A = {1, 2, 3, 4}, explain the difference between 2 ∈ A and {2} ⊆ A.
Show worked answer
2 ∈ A says the number 2 is an element of A. {2} ⊆ A says every element of the one-element set {2} belongs to A. Both statements are true, but one concerns an element and the other a subset.
Common mistakes to watch for
- The union includes the overlap; exclusive 'either but not both' is different.
- Subtract the overlap once when adding two set counts.
- Place elements outside both circles but inside the rectangle in the universal set, not outside the problem.
If one of these occurs, compare the relevant step with the worked example, then try a different question before drawing conclusions.
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More G3 Math topicsPublished by Mentora · Sources checked 12 Sept 2026
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Original public examples and answers were checked with automated mathematical/editorial QA. No individual author, human reviewer or independent expert review is recorded.