If \(A\) and \(B\) are finite and \(n(A)=n(B)\), must \(A=B\) always hold?
Answer and explanation
Correct answer: No
Having the same cardinality means only that the two finite sets contain the same number of elements; it does not mean that the elements themselves are identical. For example, \(A=\{1,2\}\) and \(B=\{3,4\}\) both have cardinality 2, but they are different sets. Equality requires every element of A to be in B and every element of B to be in A.
Frequently asked questions
What is the correct answer to this question?
No
Why is this the correct answer?
Having the same cardinality means only that the two finite sets contain the same number of elements; it does not mean that the elements themselves are identical. For example, \(A=\{1,2\}\) and \(B=\{3,4\}\) both have cardinality 2, but they are different sets. Equality requires every element of A to be in B and every element of B to be in A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
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