Sets 2

4 marks · Normal

The universal set is U = {1,2,3,4,5,6,7,8,9,10}. Let A = {x ∈ U : x is even}, B = {x ∈ U : x ≥ 6}.

(a)

List the elements of sets A and B.

[2 marks]

(b)

Find A ∩ B and (A ∪ B)′.

[2 marks]

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.

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(a) A = {2,4,6,8,10}, B = {6,7,8,9,10}

(b) A ∩ B = {6,8,10}; (A ∪ B)′ = {1,3,5}

Common mistakes: Confusing complement with intersection, omitting 0

Show mark scheme and worked solution

Marking points

B1 (a) · 1 mark · Lists all correct elements for A.

B2 (a) · 1 mark · Lists all correct elements for B.

B3 (b) · 1 mark · Corrects A ∩ B.

B4 (b) · 1 mark · Correctly finds (A ∪ B)′.

Worked solution

A = {2,4,6,8,10} (even numbers in U); B = {6,7,8,9,10} (numbers in U ≥ 6). A ∩ B = {6,8,10} (numbers in both sets). A ∪ B = {2,4,6,7,8,9,10}; (A ∪ B)′ is the elements of U not in A ∪ B: {1,3,5}.