In an exam, 82 students solved question A, 76 solved B, 69 solved C, 37 solved both A and B, 32 solved both B and C, 29 solved both C and A, and 15 solved all three. How many solved at least one question?
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Answer and explanation
Correct answer: 144
Apply the three-set inclusion-exclusion formula: n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(C ∩ A) + n(A ∩ B ∩ C). Substituting the values gives 82 + 76 + 69 − 37 − 32 − 29 + 15 = 144. Thus, 144 students solved at least one question.
Frequently asked questions
What is the correct answer to this question?
144
Why is this the correct answer?
Apply the three-set inclusion-exclusion formula: n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(C ∩ A) + n(A ∩ B ∩ C). Substituting the values gives 82 + 76 + 69 − 37 − 32 − 29 + 15 = 144. Thus, 144 students solved at least one question.
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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