If A ∩ B = A \ B, what is the correct conclusion about A?
Answer and explanation
Correct answer: A = ∅
The sets A ∩ B and A \ B represent two non-overlapping parts of A: the elements inside B and the elements outside B, respectively. Their intersection is always empty. If these two disjoint sets are equal, the common set must itself be empty. Their union is A, so A must also be empty. Hence option A is correct.
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 represent two non-overlapping parts of A: the elements inside B and the elements outside B, respectively. Their intersection is always empty. If these two disjoint sets are equal, the common set must itself be empty. Their union is A, so A must also be empty. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
