Sets (Copy)

Paper 1 Style (Short Questions – No Calculator)

Total Marks: 20
Time: 25 minutes

1. List all the elements in the set: (2 marks)
A = {x : x is a natural number less than 6}

2. The universal set ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9}
Set A = {2, 4, 6, 8}
Set B = {1, 2, 3, 4, 5}

a) Write down A ∩ B (1 mark)
b) Write down A ∪ B (1 mark)
c) Write down A′ (2 marks)

3. Given that n(A) = 14, n(B) = 9, and n(A ∩ B) = 5,
Find n(A ∪ B) (2 marks)

4. State whether the following statements are True or False: (2 marks)
a) Every element in A ∩ B is also in A.
b) The complement of the universal set ξ is ∅.

5. If A = {x : 3 ≤ x ≤ 8} where x is an integer, list the elements of A. (2 marks)

6. The universal set ξ = {a, b, c, d, e, f, g}
Set P = {a, c, e, g}

Write down:
a) n(P) (1 mark)
b) P′ (2 marks)

7. Set X = {multiples of 5 less than 30}
List all the elements of X. (2 marks)

Paper 2 Style (Structured Questions – Calculator Allowed)

Total Marks: 20
Time: 25 minutes

1. In a group of 40 students:

• 22 like Football (Set F)
• 18 like Cricket (Set C)
• 10 like both Football and Cricket

a) How many students like only Football? (2 marks)
b) How many students like neither Football nor Cricket? (2 marks)
c) Find n(F ∪ C) (2 marks)

2. The universal set ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Set A = {even numbers}
Set B = {prime numbers}

a) List the elements of A and B. (2 marks)
b) Write down A ∩ B (2 marks)
c) Find n(A ∪ B) (2 marks)

3. P = {2, 4, 6, 8} and Q = {3, 6, 9}

a) List P ∪ Q (2 marks)
b) List P ∩ Q (2 marks)
c) Find n(P′) if ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9} (2 marks)

TOTAL MARKS: 40

Marking Scheme with Detailed Explanations

Paper 1

1. A = {x : x is a natural number less than 6}
Natural numbers: 1, 2, 3, 4, 5
Answer: {1, 2, 3, 4, 5} (2 marks)

2.
a) A ∩ B = Elements common to both A and B = {2, 4} (1 mark)
b) A ∪ B = All elements in A or B = {1, 2, 3, 4, 5, 6, 8} (1 mark)
c) A′ = Elements in ξ but not in A = {1, 3, 5, 7, 9} (2 marks)

3. n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
n(A ∪ B) = 14 + 9 – 5 = 18 (2 marks)

4.
a) True (1 mark)
b) True (1 mark)
Explanation:

• Every element in A ∩ B belongs to A by definition.
• The complement of ξ is ∅ because ξ contains all possible elements.

5. A = {3, 4, 5, 6, 7, 8} (2 marks)
Explanation: List all integers from 3 to 8 inclusive.

6.
a) n(P) = Number of elements in P = 4 (1 mark)
b) P′ = Elements in ξ but not in P = {b, d, f} (2 marks)

7. X = {5, 10, 15, 20, 25} (2 marks)
Explanation: Multiples of 5 less than 30.

Paper 2

1.

• Students who like only Football = 22 – 10 = 12 (2 marks)
• Students who like either = 22 + 18 – 10 = 30
• Students who like neither = 40 – 30 = 10 (2 marks)
• n(F ∪ C) = 30 (2 marks)

2.
A = {2, 4, 6, 8, 10} (1 mark)
B = {2, 3, 5, 7} (1 mark)
a) Correct listing (2 marks)
b) A ∩ B = {2} (2 marks)
c) n(A ∪ B) = {2, 3, 4, 5, 6, 7, 8, 10} → n = 8 (2 marks)

3.
a) P ∪ Q = {2, 3, 4, 6, 8, 9} (2 marks)
b) P ∩ Q = {6} (2 marks)
c) P′ = Elements in ξ not in P = {1, 3, 5, 7, 9} → n(P′) = 5 (2 marks)