Which of the following statements is always true for any two sets A and B?
Answer and explanation
Correct answer: If A ⊆ B and B ⊆ A, then A = B
The two-way subset criterion states that if A ⊆ B and B ⊆ A, then every element of A is in B and every element of B is in A. Thus the sets have exactly the same elements, so A = B. Option B is not always true because A may equal B; a proper subset must be strictly smaller. Disjoint sets need not be equal, and equal non-empty sets usually have a non-empty intersection.
Frequently asked questions
What is the correct answer to this question?
If A ⊆ B and B ⊆ A, then A = B
Why is this the correct answer?
The two-way subset criterion states that if A ⊆ B and B ⊆ A, then every element of A is in B and every element of B is in A. Thus the sets have exactly the same elements, so A = B. Option B is not always true because A may equal B; a proper subset must be strictly smaller. Disjoint sets need not be equal, and equal non-empty sets usually have a non-empty intersection.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
