Assertion: If n(A) = n(B), then A = B. Reason: Equal cardinality always gives identical elements. Choose the correct option.
Answer and explanation
Correct answer: Both the assertion and the reason are false.
The assertion is false because equal cardinality only tells us that two sets have the same number of elements; it does not tell us that the elements themselves are identical. For example, A = {1,2} and B = {3,4} both have cardinality 2, but A ≠ B. The reason is also false for the same reason: equal size does not imply equal membership. To conclude A = B, we must show that every element of A is in B and every element of B is in A.
Frequently asked questions
What is the correct answer to this question?
Both the assertion and the reason are false.
Why is this the correct answer?
The assertion is false because equal cardinality only tells us that two sets have the same number of elements; it does not tell us that the elements themselves are identical. For example, A = {1,2} and B = {3,4} both have cardinality 2, but A ≠ B. The reason is also false for the same reason: equal size does not imply equal membership. To conclude A = B, we must show that every element of A is in B and every element of B is in A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
