If \(A=\{1,2,3,4,5,6,7\}\) and \(B=\{2,4,6,8\}\), what is \((A-B)\cup(B-A)\)?
Answer and explanation
Correct answer: \(\{1,3,5,7,8\}\)
The difference \(A-B\) contains elements in \(A\) but not in \(B\), so \(A-B=\{1,3,5,7\}\). Similarly, \(B-A\) contains elements in \(B\) but not in \(A\), so \(B-A=\{8\}\). Their union is \(\{1,3,5,7\}\cup\{8\}=\{1,3,5,7,8\}\). This operation is also called the symmetric difference: elements belonging to exactly one of the two sets.
Frequently asked questions
What is the correct answer to this question?
\(\{1,3,5,7,8\}\)
Why is this the correct answer?
The difference \(A-B\) contains elements in \(A\) but not in \(B\), so \(A-B=\{1,3,5,7\}\). Similarly, \(B-A\) contains elements in \(B\) but not in \(A\), so \(B-A=\{8\}\). Their union is \(\{1,3,5,7\}\cup\{8\}=\{1,3,5,7,8\}\). This operation is also called the symmetric difference: elements belonging to exactly one of the two sets.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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