If A ⊆ B and B ⊆ A, what conclusion follows?
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Answer and explanation
Correct answer: A = B
A ⊆ B says that every element of A belongs to B. B ⊆ A says that every element of B belongs to A. Thus the two sets contain exactly the same elements, which is the definition of equality of sets. Therefore A = B. This is commonly called the two-way subset criterion for proving set equality.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
A ⊆ B says that every element of A belongs to B. B ⊆ A says that every element of B belongs to A. Thus the two sets contain exactly the same elements, which is the definition of equality of sets. Therefore A = B. This is commonly called the two-way subset criterion for proving set equality.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
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