If n(A) = 16, n(B) = 22, and n(A ∩ B) = 7, how many elements are only in B?
Answer and explanation
Correct answer: 15
The total number of elements in B includes both the elements only in B and the elements shared with A. Hence, n(B only) = n(B) − n(A ∩ B). Substituting the given values gives 22 − 7 = 15. Therefore, option B is correct. The value 31 would be obtained from the union formula and does not represent the elements exclusively in B.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
The total number of elements in B includes both the elements only in B and the elements shared with A. Hence, n(B only) = n(B) − n(A ∩ B). Substituting the given values gives 22 − 7 = 15. Therefore, option B is correct. The value 31 would be obtained from the union formula and does not represent the elements exclusively in B.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
