If A ⊆ B, A and B are finite sets, and n(A) = n(B) = 7, what is the conclusion?
Answer and explanation
Correct answer: A = B
Because A ⊆ B, every element of A is already an element of B. If A were a proper subset of B, then B would have at least one additional element and would therefore contain more than seven elements. But both sets have cardinality 7. This is impossible, so no extra element exists in B and the two sets must be equal. Therefore A = B, making option A correct.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
Because A ⊆ B, every element of A is already an element of B. If A were a proper subset of B, then B would have at least one additional element and would therefore contain more than seven elements. But both sets have cardinality 7. This is impossible, so no extra element exists in B and the two sets must be equal. Therefore A = B, making option A correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
