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Subjects
Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)MediumLevel 18

In a survey of 90 people, 52 like tea, 47 like coffee, and 19 like both tea and coffee. How many people like neither tea nor coffee?

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Answer and explanation

Correct answer: 10

Let T be the set of people who like tea and C the set of people who like coffee. By inclusion–exclusion, n(T ∪ C) = n(T) + n(C) − n(T ∩ C) = 52 + 47 − 19 = 80. Therefore, 80 people like at least one beverage. The number who like neither is 90 − 80 = 10, so option A is correct.

Tags

setsunionintersectioninclusion-exclusionOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

10

Why is this the correct answer?

Let T be the set of people who like tea and C the set of people who like coffee. By inclusion–exclusion, n(T ∪ C) = n(T) + n(C) − n(T ∩ C) = 52 + 47 − 19 = 80. Therefore, 80 people like at least one beverage. The number who like neither is 90 − 80 = 10, so option A is correct.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).

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