If A ⊆ B, n(A) = 12, and n(B) = 31, what is n(A ∩ B)?
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Answer and explanation
Correct answer: 12
Since A ⊆ B, every element of A is also an element of B. Thus, the elements common to A and B are exactly the elements of A, so A ∩ B = A. Therefore, n(A ∩ B) = n(A) = 12. Option A is correct. The intersection cannot have more elements than the smaller set, which also rules out 31 and 43.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
Since A ⊆ B, every element of A is also an element of B. Thus, the elements common to A and B are exactly the elements of A, so A ∩ B = A. Therefore, n(A ∩ B) = n(A) = 12. Option A is correct. The intersection cannot have more elements than the smaller set, which also rules out 31 and 43.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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