In a group of 40 people, 22 like tea, 18 like coffee, and 7 like both. How many people like neither tea nor coffee?
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Answer and explanation
Correct answer: 7
Let T be the set of tea lovers and C the set of coffee lovers. By the inclusion–exclusion rule, n(T ∪ C) = n(T) + n(C) − n(T ∩ C) = 22 + 18 − 7 = 33. Therefore, the number who like neither is the total minus the union: 40 − 33 = 7. Hence, option A is correct.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
Let T be the set of tea lovers and C the set of coffee lovers. By the inclusion–exclusion rule, n(T ∪ C) = n(T) + n(C) − n(T ∩ C) = 22 + 18 − 7 = 33. Therefore, the number who like neither is the total minus the union: 40 − 33 = 7. Hence, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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