If A ⊆ B, n(A) = 9, and n(B) = 26, what is n(A ∪ B)?
Answer and explanation
Correct answer: 26
The relation A ⊆ B means that every element of A is already an element of B. When two sets have this relationship, taking their union adds no new elements to B; therefore, A ∪ B = B. Consequently, n(A ∪ B) = n(B) = 26. Option C is correct. The value 35 incorrectly adds the two cardinalities without removing the overlap.
Frequently asked questions
What is the correct answer to this question?
26
Why is this the correct answer?
The relation A ⊆ B means that every element of A is already an element of B. When two sets have this relationship, taking their union adds no new elements to B; therefore, A ∪ B = B. Consequently, n(A ∪ B) = n(B) = 26. Option C is correct. The value 35 incorrectly adds the two cardinalities without removing the overlap.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
