If A ⊆ B, B ⊆ C, and C ⊆ A, which conclusion is necessary?
Answer and explanation
Correct answer: A = B = C
Subset inclusion is transitive. From A ⊆ B and B ⊆ C, we obtain A ⊆ C. The additional condition C ⊆ A gives inclusion in both directions between A and C, so A = C. Similarly, B is contained in C and C is contained in A, which forces B to contain no extra elements. Therefore all three sets are equal: A = B = C. They may all be empty.
Frequently asked questions
What is the correct answer to this question?
A = B = C
Why is this the correct answer?
Subset inclusion is transitive. From A ⊆ B and B ⊆ C, we obtain A ⊆ C. The additional condition C ⊆ A gives inclusion in both directions between A and C, so A = C. Similarly, B is contained in C and C is contained in A, which forces B to contain no extra elements. Therefore all three sets are equal: A = B = C. They may all be empty.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
