If A ⊆ B, n(A) = 4, and n(B) = 10, what is n(A ∩ B)?
Answer and explanation
Correct answer: 4
The governing concept is the intersection of a set with a superset. Because A ⊆ B, every element of A is common to A and B. Consequently, A ∩ B = A, and its cardinality is n(A ∩ B) = n(A) = 4. The value 10 describes the larger set B, not the intersection; 6 is a subtraction distractor, and 14 incorrectly adds the cardinalities. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The governing concept is the intersection of a set with a superset. Because A ⊆ B, every element of A is common to A and B. Consequently, A ∩ B = A, and its cardinality is n(A ∩ B) = n(A) = 4. The value 10 describes the larger set B, not the intersection; 6 is a subtraction distractor, and 14 incorrectly adds the cardinalities. Therefore, 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).
