If \(A=\{1,2,3,4\}\) and \(B=\{3,4,5,6\}\), what is \((A\cup B)-(A\cap B)\)?
Answer and explanation
Correct answer: \(\{1,2,5,6\}\)
First, form the union: \(A\cup B=\{1,2,3,4,5,6\}\). Next, find the intersection: \(A\cap B=\{3,4\}\). Subtracting the intersection from the union removes the elements common to both sets, leaving \(\{1,2,5,6\}\). Thus option A is correct. This result is also called the symmetric difference because it contains elements belonging to exactly one of the two sets.
Frequently asked questions
What is the correct answer to this question?
\(\{1,2,5,6\}\)
Why is this the correct answer?
First, form the union: \(A\cup B=\{1,2,3,4,5,6\}\). Next, find the intersection: \(A\cap B=\{3,4\}\). Subtracting the intersection from the union removes the elements common to both sets, leaving \(\{1,2,5,6\}\). Thus option A is correct. This result is also called the symmetric difference because it contains elements belonging to exactly one of the two sets.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
