If \(A=\{1,2,3,4,5,6,7,8\}\) and \(B=\{2,4,6,8,10\}\), what is \((A\cup B)-(A\cap B)\)?
Answer and explanation
Correct answer: \(\{1,3,5,7,10\}\)
First, \(A\cap B=\{2,4,6,8\}\), because these elements occur in both sets. Next, \(A\cup B=\{1,2,3,4,5,6,7,8,10\}\). Removing the intersection from the union leaves the elements that belong to exactly one of the two sets: \(\{1,3,5,7,10\}\). Thus the expression is the symmetric difference of \(A\) and \(B\), so option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(\{1,3,5,7,10\}\)
Why is this the correct answer?
First, \(A\cap B=\{2,4,6,8\}\), because these elements occur in both sets. Next, \(A\cup B=\{1,2,3,4,5,6,7,8,10\}\). Removing the intersection from the union leaves the elements that belong to exactly one of the two sets: \(\{1,3,5,7,10\}\). Thus the expression is the symmetric difference of \(A\) and \(B\), 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).
