If \(A=\{1,2,4,8\}\), \(B=\{2,4,6\}\), and \(C=\{4,6,8\}\), what is \((A\cap B)\cup C\)?
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Answer and explanation
Correct answer: \(\{2,4,6,8\}\)
The parentheses require the intersection first. The elements common to \(A=\{1,2,4,8\}\) and \(B=\{2,4,6\}\) are 2 and 4, so \(A\cap B=\{2,4\}\). Taking the union with \(C=\{4,6,8\}\) gives \(\{2,4\}\cup\{4,6,8\}=\{2,4,6,8\}\). Repeated elements such as 4 are written only once in a set.
Frequently asked questions
What is the correct answer to this question?
\(\{2,4,6,8\}\)
Why is this the correct answer?
The parentheses require the intersection first. The elements common to \(A=\{1,2,4,8\}\) and \(B=\{2,4,6\}\) are 2 and 4, so \(A\cap B=\{2,4\}\). Taking the union with \(C=\{4,6,8\}\) gives \(\{2,4\}\cup\{4,6,8\}=\{2,4,6,8\}\). Repeated elements such as 4 are written only once in a set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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