If A \ B = A, which conclusion is definite?
Answer and explanation
Correct answer: A ∩ B = ∅
The set A \ B is obtained by removing from A every element that also belongs to B. If the result is still exactly A, no element of A could have been removed. Therefore A and B have no common element, which means A ∩ B = ∅. This does not imply that B is empty or that A and B are equal; B may contain elements outside A.
Frequently asked questions
What is the correct answer to this question?
A ∩ B = ∅
Why is this the correct answer?
The set A \ B is obtained by removing from A every element that also belongs to B. If the result is still exactly A, no element of A could have been removed. Therefore A and B have no common element, which means A ∩ B = ∅. This does not imply that B is empty or that A and B are equal; B may contain elements outside A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
