If \(A=\{x:x\in\mathbb{N},\ x\mid 30\}\) and \(B=\{x:x\in\mathbb{N},\ x\mid 45\}\), what is \((A\cup B)\setminus(A\cap B)\)?
Answer and explanation
Correct answer: \(\{2,6,9,10,30,45\}\)
List the positive divisors: \(A=\{1,2,3,5,6,10,15,30\}\) and \(B=\{1,3,5,9,15,45\}\). Their intersection is \(\{1,3,5,15\}\), and their union is \(\{1,2,3,5,6,9,10,15,30,45\}\). Removing the intersection from the union leaves the elements that belong to exactly one set: \(\{2,6,9,10,30,45\}\). This is the symmetric difference, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(\{2,6,9,10,30,45\}\)
Why is this the correct answer?
List the positive divisors: \(A=\{1,2,3,5,6,10,15,30\}\) and \(B=\{1,3,5,9,15,45\}\). Their intersection is \(\{1,3,5,15\}\), and their union is \(\{1,2,3,5,6,9,10,15,30,45\}\). Removing the intersection from the union leaves the elements that belong to exactly one set: \(\{2,6,9,10,30,45\}\). 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).
