To determine which of the provided sets is equivalent to the set \(\{k, 1, m, n\}\), we need to compare each option with the given set.
A set is equivalent if it contains exactly the same elements, regardless of the order.
1. Examine set \(\{k, 1, m, n\}\):
- We can observe that the elements \(k\), \(1\), \(m\), and \(n\) should match exactly with one of the provided choices.
2. Given the sets from the options:
- Option (A): \(\{5\}\)
- This set contains only one element: \(5\).
- It does not match the set \(\{k, 1, m, n\}\), which has four elements.
- Option (B): \(\{-1, 2, 6\}\)
- This set contains three elements: \(-1\), \(2\), and \(6\).
- It does not match the set \(\{k, 1, m, n\}\), which has four elements.
- Option (C): \(\{5, -1, 4, 9\}\)
- This set contains four elements: \(5\), \(-1\), \(4\), and \(9\).
- It does not match the set \(\{k, 1, m, n\}\), which should contain the elements \(k\), \(1\), \(m\), and \(n\).
- Option (D): \(\{0, 2, 4, 6, 8\}\)
- This set contains five elements: \(0\), \(2\), \(4\), \(6\), and \(8\).
- It does not match the set \(\{k, 1, m, n\}\), which has four elements.
3. Upon reviewing all the options, none of the given sets (A, B, C, or D) match the elements and the number of elements of the set \(\{k, 1, m, n\}\).
Therefore, none of the provided sets is equivalent to the set \(\{k, 1, m, n\}\).
The correct result is:
[tex]\[
\boxed{\text{None}}
\][/tex]
