In a survey, n(M) = 60, n(P) = 54, n(C) = 50, n(M ∩ P) = 25, n(P ∩ C) = 22, n(C ∩ M) = 20, and n(M ∩ P ∩ C) = 10. How many study only M?
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Answer and explanation
Correct answer: 25
The total n(M ∩ P) = 25 includes the students in all three subjects, and n(C ∩ M) = 20 also includes that same centre. To obtain only M, subtract both pairwise intersections from n(M), then add the centre once because it was subtracted twice: 60 − 25 − 20 + 10 = 25. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
25
Why is this the correct answer?
The total n(M ∩ P) = 25 includes the students in all three subjects, and n(C ∩ M) = 20 also includes that same centre. To obtain only M, subtract both pairwise intersections from n(M), then add the centre once because it was subtracted twice: 60 − 25 − 20 + 10 = 25. 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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