Skip to content

CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram

In a universal set U of 80 customers of a Pune retailer, A is the set of customers who bought tea and B is the set who bought coffee. n(A) = 45, n(B) = 38 and n(A ∩ B) = 20. How many customers bought neither tea nor coffee, i.e. n(A' ∩ B')?

The number is 17. By De Morgan's law, customers buying neither product form the complement of the union. The union is 45 + 38 − 20 = 63, so subtracting from the universal set gives 80 − 63 = 17 customers who bought neither tea nor coffee.

  1. A17Correct
  2. B37
  3. C20
  4. D63

Explanation

By De Morgan, A' ∩ B' = (A ∪ B)'. n(A ∪ B) = 45 + 38 − 20 = 63. So n(A' ∩ B') = 80 − 63 = 17. The value 37 comes from forgetting to subtract the intersection (80 − 45 − 38 is negative, so it is a different slip), while 63 is the union itself, not its complement.

Did you get it right without looking?

One question tells you little. A timed set on Set Theory, including Venn Diagram shows your real accuracy, how long you take and where you lose marks.

Practise Set Theory, including Venn DiagramFree diagnostic mock

More Set Theory, including Venn Diagram questions