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4024/22 May/Jun 2021, Question 5: Three-Set Venn Diagrams

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 7 marks

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The question, in short

Use set notation for a shaded Venn region, then work with sets ℰ, P, Q, R to complete a Venn diagram and find set elements, a count, and an empty-set statement.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 1 mark

Write set notation for the region shaded outside both circles A and B in the Venn diagram.

  1. 1Shaded region is outside both A and B
  2. 2(A ∪ B)′

Answer(A ∪ B)′

Part (bi) · 3 marks

Place the elements of ℰ into the three-circle Venn diagram for sets P, Q and R.

  1. 1P = {2, 3, 4, 6, 9, 12}, Q = {4, 8, 12}, R = {3, 4, 5, 6}
  2. 2P only: 2, 9; P ∩ Q only: 12; P ∩ Q ∩ R: 4; P ∩ R only: 3, 6
  3. 3Q only: 8; Q ∩ R only: none; R only: 5; outside: 7, 10, 11

AnswerP only: 2, 9 P ∩ Q only: 12 P ∩ Q ∩ R: 4 P ∩ R only: 3, 6 Q only: 8 Q ∩ R only: none R only: 5 Outside all three: 7, 10, 11

Part (bii) · 1 mark

List the elements belonging to P but not to Q or R.

  1. 1Q ∪ R = {3, 4, 5, 6, 8, 12}
  2. 2P ∩ (Q ∪ R)′ = {2, 9}

Answer2, 9

Part (biii) · 1 mark

Find the number of elements in the union of P and Q.

  1. 1P ∪ Q = {2, 3, 4, 6, 8, 9, 12}
  2. 2n(P ∪ Q) = 7

Answer7

Part (biv) · 1 mark

Complete the statement by writing a set expression, in set notation, that equals the empty set.

  1. 1Q ∩ R = {4} and 4 is in P
  2. 2P′ ∩ Q ∩ R = ∅

AnswerP′ ∩ Q ∩ R

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Also searched as: 4024/22/M/J/21 · 4024_s21_qp_22 · 4024 s21 22 · question 5.
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