If \(A=\{1,2\}\), \(B=\{2,3\}\), and \(C=\{3,4\}\), what is \(A\cup B\cup C\)?
Answer and explanation
Correct answer: \(\{1,2,3,4\}\)
The union of sets contains every distinct element that belongs to at least one of the sets. Starting with \(A\cup B\), we get \(\{1,2,3\}\). Taking the union of this result with \(C=\{3,4\}\) adds only 4, because 3 is already present. Therefore, \(A\cup B\cup C=\{1,2,3,4\}\). Repeated elements are written only once in a set, so option D is not acceptable.
Frequently asked questions
What is the correct answer to this question?
\(\{1,2,3,4\}\)
Why is this the correct answer?
The union of sets contains every distinct element that belongs to at least one of the sets. Starting with \(A\cup B\), we get \(\{1,2,3\}\). Taking the union of this result with \(C=\{3,4\}\) adds only 4, because 3 is already present. Therefore, \(A\cup B\cup C=\{1,2,3,4\}\). Repeated elements are written only once in a set, so option D is not acceptable.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
