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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 10

In a survey of 150 people, 85 like tea, 70 like coffee, and 40 like both tea and coffee. How many people like neither tea nor coffee?

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Answer and explanation

Correct answer: 35

Let T be the set of people who like tea and C be the set of people who like coffee. By inclusion–exclusion, n(T ∪ C) = n(T) + n(C) − n(T ∩ C) = 85 + 70 − 40 = 115. Therefore, the number who like neither is the complement of T ∪ C in the survey: 150 − 115 = 35. Hence, option A is correct.

Tags

setscomplementinclusion-exclusioncardinalityComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

35

Why is this the correct answer?

Let T be the set of people who like tea and C be the set of people who like coffee. By inclusion–exclusion, n(T ∪ C) = n(T) + n(C) − n(T ∩ C) = 85 + 70 − 40 = 115. Therefore, the number who like neither is the complement of T ∪ C in the survey: 150 − 115 = 35. Hence, option A is correct.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.

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