If A ∩ B = A and B ∩ C = B, then what is A ∩ C equal to?
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Answer and explanation
Correct answer: A
The identity A ∩ B = A means that every element of A lies in B, so A ⊆ B. Similarly, B ∩ C = B means B ⊆ C. By transitivity of subset inclusion, A ⊆ C. When A is a subset of C, intersecting A with C leaves A unchanged; therefore A ∩ C = A. No equality between A and B or between A and C is required, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
A
Why is this the correct answer?
The identity A ∩ B = A means that every element of A lies in B, so A ⊆ B. Similarly, B ∩ C = B means B ⊆ C. By transitivity of subset inclusion, A ⊆ C. When A is a subset of C, intersecting A with C leaves A unchanged; therefore A ∩ C = A. No equality between A and B or between A and C is required, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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