If \(A=\{1,2,3,4,5,6,7\}\), \(B=\{2,4,6,8\}\), and \(C=\{1,4,7,8\}\), what is the value of \((A\cup B)\cap C\)?
Answer and explanation
Correct answer: \(\{1,4,7,8\}\)
First find the union of A and B by listing every element that occurs in either set: \(A\cup B=\{1,2,3,4,5,6,7,8\}\). Next, take the intersection with C, which means retain only the elements common to this union and C. Since 1, 4, 7, and 8 all belong to the union, the result is \(\{1,4,7,8\}\). Therefore, option A is correct; option B wrongly omits 8.
Frequently asked questions
What is the correct answer to this question?
\(\{1,4,7,8\}\)
Why is this the correct answer?
First find the union of A and B by listing every element that occurs in either set: \(A\cup B=\{1,2,3,4,5,6,7,8\}\). Next, take the intersection with C, which means retain only the elements common to this union and C. Since 1, 4, 7, and 8 all belong to the union, the result is \(\{1,4,7,8\}\). Therefore, option A is correct; option B wrongly omits 8.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
