Out of 70 students, 45 study Hindi, 40 study English, and 30 study both languages. How many students study at least one of the two languages?
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Answer and explanation
Correct answer: 55
“At least one language” means the union of the Hindi and English groups. By the inclusion–exclusion principle, n(H ∪ E) = n(H) + n(E) − n(H ∩ E), because students studying both languages would otherwise be counted twice. Therefore, n(H ∪ E) = 45 + 40 − 30 = 55. Hence, option A is correct.
Frequently asked questions
What is the correct answer to this question?
55
Why is this the correct answer?
“At least one language” means the union of the Hindi and English groups. By the inclusion–exclusion principle, n(H ∪ E) = n(H) + n(E) − n(H ∩ E), because students studying both languages would otherwise be counted twice. Therefore, n(H ∪ E) = 45 + 40 − 30 = 55. Hence, 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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