In a school, 36 students learn music, 29 learn painting, and 14 learn both. How many students learn at least one activity?
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Answer and explanation
Correct answer: 51
“At least one activity” means the union of the music and painting groups. Apply n(M ∪ P) = n(M) + n(P) − n(M ∩ P). Hence n(M ∪ P) = 36 + 29 − 14 = 51. The 14 students who learn both activities must be subtracted once because they were included in both original totals. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
51
Why is this the correct answer?
“At least one activity” means the union of the music and painting groups. Apply n(M ∪ P) = n(M) + n(P) − n(M ∩ P). Hence n(M ∪ P) = 36 + 29 − 14 = 51. The 14 students who learn both activities must be subtracted once because they were included in both original totals. Therefore 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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