If B − A = B, which conclusion is always correct?
Answer and explanation
Correct answer: A ∩ B = ∅
Set difference is defined by B − A = B ∩ A′. If B − A equals all of B, removing A has removed no element from B. Therefore no element can belong to both A and B, which means A ∩ B = ∅. This conclusion says that A and B are disjoint. The other statements do not necessarily follow, so option A is the only always-correct answer.
Frequently asked questions
What is the correct answer to this question?
A ∩ B = ∅
Why is this the correct answer?
Set difference is defined by B − A = B ∩ A′. If B − A equals all of B, removing A has removed no element from B. Therefore no element can belong to both A and B, which means A ∩ B = ∅. This conclusion says that A and B are disjoint. The other statements do not necessarily follow, so option A is the only always-correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
