If A ∪ B = U and A \ B = ∅, what must be true about B?
Answer and explanation
Correct answer: B = U
The condition A \ B = ∅ means that A has no element outside B; equivalently, A ⊆ B. When A is a subset of B, their union is simply B, so A ∪ B = B. The problem also states A ∪ B = U. Combining these equalities gives B = U. The other statements may occur in special cases but are not forced by the conditions.
Frequently asked questions
What is the correct answer to this question?
B = U
Why is this the correct answer?
The condition A \ B = ∅ means that A has no element outside B; equivalently, A ⊆ B. When A is a subset of B, their union is simply B, so A ∪ B = B. The problem also states A ∪ B = U. Combining these equalities gives B = U. The other statements may occur in special cases but are not forced by the conditions.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
