If \(A=\{2,4,6,8\}\), \(B=\{4,8\}\), and \(C=\{8,10\}\), what is \((A-B)\cup C\)?
Answer and explanation
Correct answer: \(\{2,6,8,10\}\)
The difference \(A-B\) keeps elements that are in A but not in B. Removing 4 and 8 from A gives \(A-B=\{2,6\}\). Now form the union with \(C=\{8,10\}\), taking every distinct element: \(\{2,6\}\cup\{8,10\}=\{2,6,8,10\}\). Therefore option A is correct. Option B omits C, option C gives elements removed from A, and option D incorrectly retains 4, although 4 belongs to B.
Frequently asked questions
What is the correct answer to this question?
\(\{2,6,8,10\}\)
Why is this the correct answer?
The difference \(A-B\) keeps elements that are in A but not in B. Removing 4 and 8 from A gives \(A-B=\{2,6\}\). Now form the union with \(C=\{8,10\}\), taking every distinct element: \(\{2,6\}\cup\{8,10\}=\{2,6,8,10\}\). Therefore option A is correct. Option B omits C, option C gives elements removed from A, and option D incorrectly retains 4, although 4 belongs to B.
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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