In three clubs, n(A) = 72, n(B) = 68, n(C) = 61, n(A ∩ B) = 29, n(B ∩ C) = 24, n(C ∩ A) = 26, and n(A ∩ B ∩ C) = 11. How many members are only in B?
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Answer and explanation
Correct answer: 26
To find the region belonging only to B, begin with all 68 members of B. Subtract the 29 members common to A and B and the 24 members common to B and C. The 11 members in all three clubs were subtracted twice, so add them back once: only B = 68 − 29 − 24 + 11 = 26. Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
26
Why is this the correct answer?
To find the region belonging only to B, begin with all 68 members of B. Subtract the 29 members common to A and B and the 24 members common to B and C. The 11 members in all three clubs were subtracted twice, so add them back once: only B = 68 − 29 − 24 + 11 = 26. 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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