In a library, 35 students read storybooks, 20 students read poetry books, and 45 students read at least one type of book. How many students read both types of books?
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Answer and explanation
Correct answer: 10
Let S be the set of students reading storybooks and P the set reading poetry. “At least one type” means n(S ∪ P) = 45. Using n(S ∪ P) = n(S) + n(P) − n(S ∩ P), we get 45 = 35 + 20 − n(S ∩ P). Hence n(S ∩ P) = 10. Therefore, 10 students read both types.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
Let S be the set of students reading storybooks and P the set reading poetry. “At least one type” means n(S ∪ P) = 45. Using n(S ∪ P) = n(S) + n(P) − n(S ∩ P), we get 45 = 35 + 20 − n(S ∩ P). Hence n(S ∩ P) = 10. Therefore, 10 students read both types.
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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