If A and B are finite sets such that A is a subset of B and n(A) = n(B), which conclusion is correct?
Answer and explanation
Correct answer: A = B
Because A is a subset of B, every element of A is already contained in B. If A were a proper subset, B would contain at least one additional element, and therefore n(B) would be greater than n(A). The given equality n(A) = n(B), together with finiteness, rules out any additional element. Hence the two sets contain exactly the same elements, so A = B. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
Because A is a subset of B, every element of A is already contained in B. If A were a proper subset, B would contain at least one additional element, and therefore n(B) would be greater than n(A). The given equality n(A) = n(B), together with finiteness, rules out any additional element. Hence the two sets contain exactly the same elements, so A = B. Therefore option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
