Question 1 Easy
A = {3, 6, 9, 12}. Work out n(A).
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Answer: 4
- Count the members.
- There are 4 members.
- Method (1): Count the members.
- Accuracy (1): There are 4 members.
Sets and set notation practice questions with answers
A second set of sets and set notation questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.
More questions
Question 2 Easy
Is 7 ∈ {2, 3, 5, 7, 11}? Answer yes or no.
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Answer: yes
- The symbol ∈ means is a member of.
- 7 is in the list.
- Method (1): The symbol ∈ means is a member of.
- Accuracy (1): 7 is in the list.
Question 3 Medium
ξ is the whole numbers from 1 to 10. List the prime numbers in ξ.
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Answer: {2, 3, 5, 7}
- A prime has exactly two factors.
- 1 is not prime, so the primes are 2, 3, 5 and 7.
- Method (1): A prime has exactly two factors.
- Accuracy (1): 1 is not prime, so the primes are 2, 3, 5 and 7.
Question 4 Medium
n(ξ) = 30 and n(A) = 12. Work out n(A').
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Answer: 18
- The complement is everything outside A.
- 30 - 12 = 18.
- Method (1): The complement is everything outside A.
- Accuracy (1): 30 - 12 = 18.
Question 5 Hard
ξ is the whole numbers from 1 to 20. A is the set of multiples of 5. B is the set of even numbers. Work out n(A ∩ B).
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Answer: 2
- A = {5, 10, 15, 20} and B has the even numbers.
- The members in both are 10 and 20.
- Method (1): A = {5, 10, 15, 20} and B has the even numbers.
- Accuracy (1): The members in both are 10 and 20.
Question 6 Hard
ξ is the whole numbers from 1 to 12. A is the set of multiples of 3. Work out the probability that a number chosen at random is in A'.
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Answer: 2/3
- A has 4 members, so A' has 12 - 4 = 8.
- 8/12 simplifies to 2/3.
- Method (1): A has 4 members, so A' has 12 - 4 = 8.
- Accuracy (1): 8/12 simplifies to 2/3.
Exam-style question
A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.
Exam-style question 13 marks
n(A) = 14, n(B) = 11 and n(A ∩ B) = 5. Work out n(A ∪ B).
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Answer: 20
- Add the two counts: 14 + 11 = 25.
- Take away the overlap: 25 - 5 = 20.
- Method (1): Adds n(A) and n(B)
- Method (1): Subtracts n(A ∩ B)
- Accuracy (1): 20
Quick checks
Short one-step questions. Pick an option before you open the answer.
Check 1
What does the symbol ∈ mean?
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Is a member of. Is a member of.
Check 2
What does the symbol ∉ mean?
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Is not a member of. Is not a member of.
Check 3
What is the universal set?
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The set of everything in the question, written ξ. The set of everything in the question, written ξ.
Check 4
What does A ∪ B mean?
- The union: members in A or in B or in both.
- The intersection: members in both A and B.
- Every member of A is also in B.
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The union: members in A or in B or in both. The union: members in A or in B or in both.
Check 5
What does A ∩ B mean?
- The intersection: members in both A and B.
- Every member of A is also in B.
- The union: members in A or in B or in both.
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The intersection: members in both A and B. The intersection: members in both A and B.
Check 6
What does A' mean?
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The complement: everything in ξ that is not in A. The complement: everything in ξ that is not in A.
Check 7
What does n(A) mean?
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The number of members in A. It is a single number. The number of members in A. It is a single number.
Check 8
What is the empty set?
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The set with no members, written ∅ or { }. The set with no members, written ∅ or { }.
Check 9
What does A ⊂ B mean?
- The union: members in A or in B or in both.
- Every member of A is also in B.
- The intersection: members in both A and B.
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Every member of A is also in B. Every member of A is also in B.
Check 10
How do you work out n(A ∪ B)?
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n(A) + n(B) - n(A ∩ B). n(A) + n(B) - n(A ∩ B).
Check 11
Why do you subtract n(A ∩ B)?
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The members in both sets were counted twice. The members in both sets were counted twice.
Check 12
How do you find n(A')?
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n(ξ) - n(A). n(ξ) - n(A).
Check 13
Is 1 a prime number?
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No. A prime has exactly two factors and 1 has only one. No. A prime has exactly two factors and 1 has only one.
Check 14
What does {x : x > 3} mean?
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The set of all x such that x is greater than 3. The set of all x such that x is greater than 3.
Check 15
Does the order of the members of a set matter?
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No. {1, 2, 3} and {3, 1, 2} are the same set. No. {1, 2, 3} and {3, 1, 2} are the same set.
Check 16
Can a member be written twice in a set?
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No. Each member is written once. No. Each member is written once.
Keep going with Sets and set notation
Practise free
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