If A − B = A and B − C = B, which of the following statements must be true?
Answer and explanation
Correct answer: (A ∩ B = ∅) ∧ (B ∩ C = ∅)
The equality A − B = A says that removing B from A removes nothing. Therefore, A and B have no common element, so A ∩ B = ∅. In the same way, B − C = B means that removing C from B changes nothing, which gives B ∩ C = ∅. These are exactly the two claims in option A. No inclusion, equality, or union relation among all three sets is forced.
Frequently asked questions
What is the correct answer to this question?
(A ∩ B = ∅) ∧ (B ∩ C = ∅)
Why is this the correct answer?
The equality A − B = A says that removing B from A removes nothing. Therefore, A and B have no common element, so A ∩ B = ∅. In the same way, B − C = B means that removing C from B changes nothing, which gives B ∩ C = ∅. These are exactly the two claims in option A. No inclusion, equality, or union relation among all three sets is forced.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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