If A ∪ B = A \ B, what is necessarily true about B?
Answer and explanation
Correct answer: B = ∅
Every element of B belongs to A ∪ B, so the left side contains all elements of B. However, A \ B is defined as the set of elements in A that are not in B; it contains no element of B. If the two sides are equal, B can have no elements at all. Hence B = ∅. The other options are not forced by the given equality.
Frequently asked questions
What is the correct answer to this question?
B = ∅
Why is this the correct answer?
Every element of B belongs to A ∪ B, so the left side contains all elements of B. However, A \ B is defined as the set of elements in A that are not in B; it contains no element of B. If the two sides are equal, B can have no elements at all. Hence B = ∅. The other options are not forced by the given equality.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
