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Cambridge IGCSE Maths (0580) · Topic 1: Number · 1.2

Cambridge IGCSE Maths 0580 Sets and Venn Diagrams Questions

Sets and Venn Diagrams questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.

Practise sets and Venn diagrams →Sets and Venn Diagrams notes

What the syllabus asks

Summarised in our own words: check the exact wording in the official 0580 syllabus.

Sets and Venn Diagrams questions: Core

For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).

Question 1 Core non-calculator · easy

ℰ \(= \{1, 2, 3, \ldots, 15\}\), \(A = \{\text{odd numbers}\}\) and \(B = \{\text{multiples of } 3\}\).
(a) List the members of \(A \cap B\).
(b) Find \(n(A \cup B)\).

Show the worked answer
  1. \(A = \{1, 3, 5, 7, 9, 11, 13, 15\}\) and \(B = \{3, 6, 9, 12, 15\}\).
  2. (a) In both sets: \(A \cap B = \{3, 9, 15\}\).
  3. (b) \(n(A \cup B) = n(A) + n(B) - n(A \cap B) = 8 + 5 - 3 = 10\).

Answer: (a) \(\{3, 9, 15\}\) (b) \(10\)

Question 2 Core non-calculator · easy

There are \(30\) students in a class. \(18\) study French, \(15\) study Spanish and \(7\) study both.
How many students study neither French nor Spanish?

Show the worked answer
  1. French only: \(18 - 7 = 11\). Spanish only: \(15 - 7 = 8\).
  2. At least one language: \(11 + 7 + 8 = 26\).
  3. Neither: \(30 - 26 = 4\).

Answer: \(4\)

Question 3 Core calculator · easy · 2 marks

\(n(A) = 12\), \(n(B) = 9\) and \(n(A \cap B) = 4\). Find \(n(A \cup B)\).

Show the answer and mark scheme
  • M1 12 + 9 − 4, or a Venn diagram with 8, 4, 5
  • A1 17

Answer: \(17\)

Question 4 Core non-calculator · medium

ℰ \(= \{1, 2, 3, \ldots, 10\}\) and \(P = \{\text{prime numbers}\}\).
List the members of \(P'\).

Show the worked answer
  1. The primes up to \(10\) are \(2, 3, 5, 7\), so \(P = \{2, 3, 5, 7\}\).
  2. \(P'\) is everything in ℰ that is not in \(P\): \(\{1, 4, 6, 8, 9, 10\}\). (\(1\) is not prime.)

Answer: \(\{1, 4, 6, 8, 9, 10\}\)

Question 5 Core non-calculator · medium

\(60\) people were asked if they drink tea or coffee. \(35\) drink tea, \(30\) drink coffee and \(8\) drink neither.
How many drink both?

Show the worked answer
  1. Let \(x\) drink both. Then tea only is \(35 - x\) and coffee only is \(30 - x\).
  2. \((35 - x) + x + (30 - x) + 8 = 60\), so \(73 - x = 60\).
  3. \(x = 13\).

Answer: \(13\)

Question 6 Core non-calculator · medium

\(n(\)ℰ\() = 40\), \(n(A) = 22\), \(n(B) = 17\) and \(n(A \cap B) = 6\).
Find \(n((A \cup B)')\).

Show the worked answer
  1. \(n(A \cup B) = 22 + 17 - 6 = 33\).
  2. \(n((A \cup B)') = 40 - 33 = 7\).

Answer: \(7\)

Question 7 Core non-calculator · medium · 3 marks

n(ℰ) \(= 40\), \(n(A) = 18\) and \(n(B) = 22\). There are 7 elements in neither \(A\) nor \(B\). Find \(n(A \cap B)\).

Show the answer and mark scheme
  • M1 n(A ∪ B) = 40 − 7 = 33
  • M1 18 + 22 − 33
  • A1 7

Answer: \(7\)

Question 8 Core calculator · medium · 2 marks

Use set notation to describe

(a) the elements that are in \(A\) but not in \(B\)

(b) the elements that are in neither \(A\) nor \(B\).

Show the answer and mark scheme
  • B1 (a) A ∩ B′
  • B1 (b) (A ∪ B)′ oe, e.g. A′ ∩ B′

Answer: (a) \(A \cap B'\) (b) \((A \cup B)'\)

Question 9 Core non-calculator · hard

ℰ \(= \{1, 2, 3, \ldots, 12\}\), \(A = \{\text{factors of } 12\}\) and \(B = \{\text{even numbers}\}\).
List the members of
(a) \(A' \cap B\)
(b) \((A \cup B)'\)

Show the worked answer
  1. \(A = \{1, 2, 3, 4, 6, 12\}\) and \(B = \{2, 4, 6, 8, 10, 12\}\).
  2. (a) Even numbers that are not factors of \(12\): \(\{8, 10\}\).
  3. (b) \(A \cup B = \{1, 2, 3, 4, 6, 8, 10, 12\}\), so \((A \cup B)' = \{5, 7, 9, 11\}\).

Answer: (a) \(\{8, 10\}\) (b) \(\{5, 7, 9, 11\}\)

Sets and Venn Diagrams questions: Extended

Extended content, for Papers 2 and 4. Core students can skip these.

Question 10 Extended non-calculator · hard

ℰ \(= \{1, 2, 3, \ldots, 20\}\), \(A = \{\text{multiples of } 2\}\), \(B = \{\text{multiples of } 3\}\) and \(C = \{\text{multiples of } 5\}\).
(a) List the members of \(A \cap B \cap C'\).
(b) Find \(n(A \cup B \cup C)\).

Show the worked answer
  1. (a) \(A \cap B\) is the multiples of \(6\): \(\{6, 12, 18\}\). None of them is a multiple of \(5\), so all three are in \(C'\).
  2. (b) Count the numbers from \(1\) to \(20\) that are a multiple of \(2\), \(3\) or \(5\): \(2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20\).
  3. That is \(14\) numbers. (Only \(1, 7, 11, 13, 17, 19\) are outside all three sets.)

Answer: (a) \(\{6, 12, 18\}\) (b) \(14\)

Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).

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Questions students ask

Which Cambridge 0580 papers can test sets and Venn diagrams?

Sets and Venn Diagrams is on both tiers (syllabus 1.2), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.

Are these Cambridge past-paper questions?

No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.

Where can I practise more sets and Venn diagrams questions?

In the 0580 practice for topic 1 (Number), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.

More number questions