If A \ B = A, which statement must be true?
Answer and explanation
Correct answer: A ∩ B = ∅
The difference A \ B contains the elements of A that are not in B. If removing all elements of B from A leaves A unchanged, then no element of A can have belonged to B. Equivalently, there is no common element between the sets, so A ∩ B = ∅. The condition does not require B to be contained in A, nor does it imply that A is contained in B or that their union equals A.
Frequently asked questions
What is the correct answer to this question?
A ∩ B = ∅
Why is this the correct answer?
The difference A \ B contains the elements of A that are not in B. If removing all elements of B from A leaves A unchanged, then no element of A can have belonged to B. Equivalently, there is no common element between the sets, so A ∩ B = ∅. The condition does not require B to be contained in A, nor does it imply that A is contained in B or that their union equals 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).
