If n(A) = 9, n(B) = 7, and n(A ∩ B) = 2, what is the total number of elements that belong only to A and only to B?
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Answer and explanation
Correct answer: 12
The two sets contain a common part of 2 elements. Therefore, the elements only in A are n(A) − n(A ∩ B) = 9 − 2 = 7, and the elements only in B are n(B) − n(A ∩ B) = 7 − 2 = 5. Adding these two separate regions gives 7 + 5 = 12, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
The two sets contain a common part of 2 elements. Therefore, the elements only in A are n(A) − n(A ∩ B) = 9 − 2 = 7, and the elements only in B are n(B) − n(A ∩ B) = 7 − 2 = 5. Adding these two separate regions gives 7 + 5 = 12, so option B 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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