Which statement is necessary and sufficient for two sets to be equal?
Answer and explanation
Correct answer: They contain exactly the same elements.
Two sets are equal precisely when every element of the first set belongs to the second set and every element of the second belongs to the first. In other words, their elements must be exactly the same. Equal cardinality alone does not guarantee equality; for example, {1, 2} and {a, b} have the same size but different elements. The order and names used to write sets are irrelevant.
Frequently asked questions
What is the correct answer to this question?
They contain exactly the same elements.
Why is this the correct answer?
Two sets are equal precisely when every element of the first set belongs to the second set and every element of the second belongs to the first. In other words, their elements must be exactly the same. Equal cardinality alone does not guarantee equality; for example, {1, 2} and {a, b} have the same size but different elements. The order and names used to write sets are irrelevant.
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.
