If \(A=\{1,4,7,10\}\), \(B=\{2,4,8,10\}\), and \(C=\{4,10,12\}\), what is \((A\cup B)\cap C\)?
Answer and explanation
Correct answer: \(\{4,10\}\)
First form the union: \(A\cup B=\{1,2,4,7,8,10\}\), containing every distinct element in A or B. Next intersect this result with \(C=\{4,10,12\}\), retaining only elements common to both sets. The common elements are 4 and 10, while 12 is absent from the union. Thus \((A\cup B)\cap C=\{4,10\}\), so option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(\{4,10\}\)
Why is this the correct answer?
First form the union: \(A\cup B=\{1,2,4,7,8,10\}\), containing every distinct element in A or B. Next intersect this result with \(C=\{4,10,12\}\), retaining only elements common to both sets. The common elements are 4 and 10, while 12 is absent from the union. Thus \((A\cup B)\cap C=\{4,10\}\), 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).
