If A ⊆ B, B ⊆ C, and A = C, which conclusion about A, B, and C is correct?
Answer and explanation
Correct answer: A = B = C
Use the antisymmetry property of set inclusion. The given relations produce A ⊆ B ⊆ C, while A = C changes this chain into A ⊆ B ⊆ A. Thus both A ⊆ B and B ⊆ A hold, so A = B. Since A = C is already given, all three sets are equal. Option A is correct. Options B and C incorrectly assert proper inclusion, and D contradicts the stated equality A = C.
Frequently asked questions
What is the correct answer to this question?
A = B = C
Why is this the correct answer?
Use the antisymmetry property of set inclusion. The given relations produce A ⊆ B ⊆ C, while A = C changes this chain into A ⊆ B ⊆ A. Thus both A ⊆ B and B ⊆ A hold, so A = B. Since A = C is already given, all three sets are equal. Option A is correct. Options B and C incorrectly assert proper inclusion, and D contradicts the stated equality A = C.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
