IGCSE Math RevisionWorked example 1: Set notation
\(A=\{2,4,6,8\}\). Is \(6\in A\)? Find \(n(A)\).
Solution
- 6 is a member of A, so \(6\in A\) is true.
- A has 4 elements: \(n(A)=4\).
Answer: True; 4
Tip: ∈ means 'is a member of'.
Edexcel IGCSE Maths (4MA1) · Unit 6: Statistics & Probability
IGCSE Maths Sets and Venn Diagrams Questions and Answers
Sets and Venn Diagrams questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 6 worked examples first, then try the 3 exam-style questions yourself and check your working against the mark scheme.
- 6 worked examples
- 3 questions with mark schemes
- Higher tier · calculator allowed
- Free, no sign-in
What this topic covers
- Sets 1: Set Language & Notation: Sets, union, intersection notation.
- Sets 2: Set Arithmetic (Union/Intersection): |A ∪ B| = |A| + |B| − |A ∩ B|.
- Sets 3: Set Listing & Cardinality: Set notation with universal set 𝓔 and complements.
- Venn Diagrams 1: Representing Elements: Two- and three-set Venn diagrams from data.
- Venn Diagrams 2: Cardinality & Counting: Using Venn regions to count sub-sets.
- Venn Diagrams 3: Problem Solving: Word problems using Venn diagrams to organise data.
Sets and Venn Diagrams worked examples
Worked example 2: Union and intersection
\(A=\{1,2,3,4,5\}\), \(B=\{4,5,6,7\}\). Find \(A\cup B\) and \(A\cap B\).
Solution
- Union: everything in either set, \(\{1,2,3,4,5,6,7\}\).
- Intersection: in both, \(\{4,5\}\).
Answer: \(\{1,\ldots,7\}\); \(\{4,5\}\)
Tip: ∪ is 'or', ∩ is 'and'.
Worked example 3: Complement
\(\mathscr{E}=\{1,2,\ldots,12\}\) and \(A=\{\text{even numbers}\}\). List \(A'\) and find \(n(A')\).
Solution
- \(A'\) is everything in \(\mathscr{E}\) not in A: \(\{1,3,5,7,9,11\}\).
- \(n(A')=6\).
Answer: \(\{1,3,5,7,9,11\}\); 6
Tip: n(A) + n(A′) = n(ℰ).
Worked example 4: Placing elements in a Venn diagram
\(\mathscr{E}=\{1,\ldots,10\}\), P = {prime numbers}, Q = {odd numbers}. Place the elements in a Venn diagram.
Solution
- \(P\cap Q=\{3,5,7\}\).
- P only: \(\{2\}\); Q only: \(\{1,9\}\).
- Neither: \(\{4,6,8,10\}\).
Answer: Middle 3, 5, 7; P only 2; Q only 1, 9; outside 4, 6, 8, 10
Tip: Fill the intersection first.
Worked example 5: Counting with a Venn diagram
\(n(A)=15\), \(n(B)=12\), \(n(A\cup B)=20\). Find \(n(A\cap B)\).
Solution
- \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\).
- \(20=27-n(A\cap B)\), so \(n(A\cap B)=7\).
Answer: 7
Tip: The intersection is counted twice in n(A) + n(B).
Worked example 6: Venn problem solving
In a class of 30, 18 study French, 15 study Spanish and 4 study neither. How many study both?
Solution
- Studying at least one: \(30-4=26\).
- Both \(=18+15-26=7\).
Answer: 7
Tip: Draw the diagram and check all regions total 30.
Sets and Venn Diagrams exam-style questions
Try each question before you open the answer. The mark schemes use Edexcel-style marks: M for method, A for accuracy (after the method mark), B for an independent result.
Question 1
A sports centre asked 50 of its members which facilities they use. 27 use the gym, 21 use the pool and 6 use both the gym and the pool. How many of these members use neither the gym nor the pool?
Show the answer and mark scheme
- M1 27 + 21 − 6 = 42 (or 21 + 6 + 15 in the Venn diagram)
- A1 8
Answer: 8
Question 2
\( n(\xi) = 90 \), \( n(A) = 48 \), \( n(B) = 35 \) and \( n(A' \cap B') = 22 \). Find \( n(A \cap B) \).
Show the answer and mark scheme
- M1 n(A ∪ B) = 90 − 22 = 68
- M1 48 + 35 − 68
- A1 15
Answer: 15
Question 3
120 guests were asked which drinks they had: tea (T), coffee (C) and juice (J). 55 had tea, 62 had coffee and 40 had juice. 30 had both tea and coffee, 20 had both coffee and juice, and 18 had both tea and juice; these numbers include the 12 guests who had all three. How many guests had none of the three drinks?
Show the answer and mark scheme
- M1 12 in the centre and 18, 8, 6 in the 'exactly two' regions
- M1 T only 19, C only 24, J only 14
- M1 total inside the circles 101 (or 55 + 62 + 40 − 30 − 20 − 18 + 12)
- A1 19
Answer: 19
Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.
Revise sets and Venn diagrams for the exam
- Unit 6 practice: Statistics & Probability in the student hub (more questions with mark schemes)
- IGCSE Maths revision notes for this topic and the IGCSE Maths formula sheet
- Edexcel IGCSE Maths 4MA1 past papers to practise under exam conditions
- IGCSE Maths 4MA1 examiner report summary: where students lose marks
Questions students ask
Which Edexcel IGCSE Maths papers test sets and Venn diagrams?
Either Higher tier paper, 1H or 2H, can test sets and Venn diagrams: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.
Where can I practise more sets and Venn diagrams questions?
In the IGCSE student hub: Unit 6 (Statistics & Probability) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.