If \(A\subseteq B\), then \((A\cup B)\setminus(A\cap B)\) is equal to which set?
Answer and explanation
Correct answer: \(B\setminus A\)
The condition \(A\subseteq B\) means every element of A is already in B. Consequently, the union is \(A\cup B=B\), while the intersection is \(A\cap B=A\). Substituting these identities into the expression gives \((A\cup B)\setminus(A\cap B)=B\setminus A\). This is precisely the part of B that is not contained in A.
Frequently asked questions
What is the correct answer to this question?
\(B\setminus A\)
Why is this the correct answer?
The condition \(A\subseteq B\) means every element of A is already in B. Consequently, the union is \(A\cup B=B\), while the intersection is \(A\cap B=A\). Substituting these identities into the expression gives \((A\cup B)\setminus(A\cap B)=B\setminus A\). This is precisely the part of B that is not contained in A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
