Under which condition are two sets A and B called equal?
Answer and explanation
Correct answer: A ⊆ B and B ⊆ A
Two sets are equal precisely when they contain exactly the same elements. This is equivalent to saying that every element of A belongs to B and every element of B belongs to A; therefore, A ⊆ B and B ⊆ A. Merely having the same number of elements does not ensure equality, because different sets can have equal cardinality. Disjointness means that the sets have no common element, not that they are equal.
Frequently asked questions
What is the correct answer to this question?
A ⊆ B and B ⊆ A
Why is this the correct answer?
Two sets are equal precisely when they contain exactly the same elements. This is equivalent to saying that every element of A belongs to B and every element of B belongs to A; therefore, A ⊆ B and B ⊆ A. Merely having the same number of elements does not ensure equality, because different sets can have equal cardinality. Disjointness means that the sets have no common element, not that they are equal.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
