If A ⊆ B, n(A) = 38, n(B) = 91, and n(U) = 130, what is n(Bᶜ)?
Answer and explanation
Correct answer: 39
The complement Bᶜ consists of all elements in the universal set U that are not in B. Therefore, its cardinality is found by subtracting the number of elements in B from the number of elements in U: n(Bᶜ) = n(U) − n(B) = 130 − 91 = 39. The information A ⊆ B and n(A) = 38 is not needed for this calculation. Thus, option A is correct.
Frequently asked questions
What is the correct answer to this question?
39
Why is this the correct answer?
The complement Bᶜ consists of all elements in the universal set U that are not in B. Therefore, its cardinality is found by subtracting the number of elements in B from the number of elements in U: n(Bᶜ) = n(U) − n(B) = 130 − 91 = 39. The information A ⊆ B and n(A) = 38 is not needed for this calculation. Thus, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
