CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram
In a Venn diagram, n(A) = 30, n(B) = 25 and n(A ∩ B) = 10. What is n(A Δ B), the number of elements in exactly one of the two sets?
The number of elements in exactly one set is 35. Only A has 20 elements and only B has 15 elements, so together they give 35. Subtracting the overlap twice from the sum of 55 gives the same figure.
- A35
- B45Correct
- C25
- D55
Explanation
Only A = 30-10 = 20 and only B = 25-10 = 15, so the total is 35. Alternatively 30+25-2(10) = 35. Option 45 is the union, which wrongly includes the overlap once; 35 is correct, so the key must be 35.
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