If A ∩ B = A \ B, which conclusion about A is correct?
Answer and explanation
Correct answer: A = ∅
The sets A ∩ B and A \ B are always disjoint: an element cannot be both in B and outside B. If two disjoint sets are equal, their common set must contain no elements. Therefore A ∩ B = A \ B = ∅. Since A \ B = ∅ alone does not always imply A = ∅, the equality with A ∩ B is essential here, and option A is the only necessary conclusion.
Frequently asked questions
What is the correct answer to this question?
A = ∅
Why is this the correct answer?
The sets A ∩ B and A \ B are always disjoint: an element cannot be both in B and outside B. If two disjoint sets are equal, their common set must contain no elements. Therefore A ∩ B = A \ B = ∅. Since A \ B = ∅ alone does not always imply A = ∅, the equality with A ∩ B is essential here, and option A is the only necessary conclusion.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
