If n(A) = 24, n(B) = 20, and n(A ∩ B) = 6, what is the combined number of elements that are only in A and only in B?
Answer and explanation
Correct answer: 32
The elements only in A are counted by n(A − B) = n(A) − n(A ∩ B) = 24 − 6 = 18. Similarly, the elements only in B are n(B − A) = n(B) − n(A ∩ B) = 20 − 6 = 14. These two regions do not overlap, so their combined number is 18 + 14 = 32. Thus option B is correct. The value 38 is the union, not the sum of the two exclusive regions.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
The elements only in A are counted by n(A − B) = n(A) − n(A ∩ B) = 24 − 6 = 18. Similarly, the elements only in B are n(B − A) = n(B) − n(A ∩ B) = 20 − 6 = 14. These two regions do not overlap, so their combined number is 18 + 14 = 32. Thus option B is correct. The value 38 is the union, not the sum of the two exclusive regions.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
