In which situation can A \ B = A ∩ B be true?
Answer and explanation
Correct answer: A = ∅
The sets A \ B and A ∩ B are always disjoint: an element outside B cannot at the same time be inside B. If two disjoint sets are equal, their common set must be empty. Thus both sides must be empty. In particular, A \ B = ∅ and A ∩ B = ∅ force A = ∅, so option A is the valid situation. The other choices leave a nonempty side or make the two sides different.
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 outside B cannot at the same time be inside B. If two disjoint sets are equal, their common set must be empty. Thus both sides must be empty. In particular, A \ B = ∅ and A ∩ B = ∅ force A = ∅, so option A is the valid situation. The other choices leave a nonempty side or make the two sides different.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
