If \(A\subseteq B\), then what is \(A\cup(B\setminus A)\) equal to?
Answer and explanation
Correct answer: \(B\)
Because \(A\subseteq B\), every element of A is already an element of B. The difference \(B\setminus A\) contains precisely those elements of B that are not in A. Thus, A and \(B\setminus A\) are disjoint parts whose union contains every element of B exactly once. Therefore, \(A\cup(B\setminus A)=B\). This is a standard partition identity for a subset and its remainder.
Frequently asked questions
What is the correct answer to this question?
\(B\)
Why is this the correct answer?
Because \(A\subseteq B\), every element of A is already an element of B. The difference \(B\setminus A\) contains precisely those elements of B that are not in A. Thus, A and \(B\setminus A\) are disjoint parts whose union contains every element of B exactly once. Therefore, \(A\cup(B\setminus A)=B\). This is a standard partition identity for a subset and its remainder.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
