If A ⊆ B, then what is (A ∪ B) − A equal to?
Answer and explanation
Correct answer: B − A
Since A ⊆ B, every element of A is already in B, so A ∪ B = B. Substituting this into the expression gives (A ∪ B) − A = B − A. This is the portion of B outside A. It is not necessarily empty: it becomes empty only when A = B. Therefore, option A correctly applies the subset property and the definition of set difference.
Frequently asked questions
What is the correct answer to this question?
B − A
Why is this the correct answer?
Since A ⊆ B, every element of A is already in B, so A ∪ B = B. Substituting this into the expression gives (A ∪ B) − A = B − A. This is the portion of B outside A. It is not necessarily empty: it becomes empty only when A = B. Therefore, option A correctly applies the subset property and the definition of set difference.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
