Sets 2
3 marks · NormalGiven the Venn diagram representing three sets A, B and C within universal set U:
Shade the region representing (A ∩ B′ ) ∪ (B ∩ C).
How many distinct regions are there in a three-set Venn diagram?
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(a) Shaded regions covering all elements in (A ∩ B′ ) and also all in (B ∩ C) (shaded union of those two areas). · must show (A ∩ B′ ), (B ∩ C)
(b) 8
Must show: Shaded regions for (A ∩ B′ ) and (B ∩ C)
Common mistakes: Not shading union correctly
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Marking points
B1 (a) · 2 marks · Correct shading for both (A ∩ B′ ) and (B ∩ C), combined as union.
B1 (b) · 1 mark · Correct answer 8 for number of regions.
Worked solution
a) Shade the region in the Venn diagram: (A ∩ B′ ) is the part inside A but outside B; (B ∩ C) is the overlap of B and C. Shade both regions.
b) In a 3-set Venn diagram, there are 8 distinct regions (each possibility of inclusion/exclusion for the three sets).