In an exam, among 180 students, 97 solved A, 88 solved B, 82 solved C, 41 solved A and B, 36 solved B and C, 34 solved C and A, and 18 solved all three. How many solved at least one question?
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Answer and explanation
Correct answer: 174
Use the inclusion-exclusion formula for three sets: n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(C ∩ A) + n(A ∩ B ∩ C). Substitution gives 97 + 88 + 82 − 41 − 36 − 34 + 18 = 174. The triple intersection is added once at the end because it was subtracted too many times. Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
174
Why is this the correct answer?
Use the inclusion-exclusion formula for three sets: n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(C ∩ A) + n(A ∩ B ∩ C). Substitution gives 97 + 88 + 82 − 41 − 36 − 34 + 18 = 174. The triple intersection is added once at the end because it was subtracted too many times. Thus 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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