Sets 2

3 marks · Easy

The universal set is S = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Let A = {1, 3, 5, 7, 9} and B = {3, 4, 5, 6}.

(a)

List the set A ∩ B.

[1 mark]

(b)

Find n(A ∪ B).

[1 mark]

(c)

List the set (A ∪ B)′.

[1 mark]

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

(a) {3, 5}

(b) 7

Common mistakes: Forgetting to include all elements in the union or complement

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Identifies A∩B correctly as {3, 5}

A1 (b) · 1 mark · Finds n(A∪B) = 7.

A1 (c) · 1 mark · Lists complement as {2, 8, 9}.

Worked solution

a) A ∩ B = {3, 5} (numbers in both sets).

b) A ∪ B = {1, 3, 4, 5, 6, 7, 9}, so n(A ∪ B) = 7.

c) (A ∪ B)′ = S \ (A ∪ B) = {2, 8, 9}.