If A ⊆ B, then A ∪ (B \ A) is equal to which set?
Answer and explanation
Correct answer: B
Because A is a subset of B, every element of B is either already in A or belongs to B but not to A. Thus the two disjoint parts A and B \ A together partition B. Their union contains every element of B and contains nothing outside B. Consequently, A ∪ (B \ A) = B. This identity depends on the given subset condition; without A ⊆ B, it would not generally hold.
Frequently asked questions
What is the correct answer to this question?
B
Why is this the correct answer?
Because A is a subset of B, every element of B is either already in A or belongs to B but not to A. Thus the two disjoint parts A and B \ A together partition B. Their union contains every element of B and contains nothing outside B. Consequently, A ∪ (B \ A) = B. This identity depends on the given subset condition; without A ⊆ B, it would not generally hold.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
