If \(A=\{a,b,c,d\}\) and \(B=\{b,d,e\}\), what is \((A\setminus B)\cup(B\setminus A)\)?
Answer and explanation
Correct answer: \(\{a,c,e\}\)
First find each difference separately. Elements in \(A\) but not \(B\) are \(a,c\), so \(A\setminus B=\{a,c\}\). Elements in \(B\) but not \(A\) are \(e\), so \(B\setminus A=\{e\}\). Their union is therefore \(\{a,c\}\cup\{e\}=\{a,c,e\}\). This is the symmetric difference, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(\{a,c,e\}\)
Why is this the correct answer?
First find each difference separately. Elements in \(A\) but not \(B\) are \(a,c\), so \(A\setminus B=\{a,c\}\). Elements in \(B\) but not \(A\) are \(e\), so \(B\setminus A=\{e\}\). Their union is therefore \(\{a,c\}\cup\{e\}=\{a,c,e\}\). This is the symmetric difference, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
