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What is the congruence class $[n_5]$ (that is, the equivalence class of n with respect to congruence modulo 5) when n is 6

I think it would be like $[6]_{5} \equiv[1]_5$ which is set of all numbers which leave a remainder of 1 when divided by 5.

but in rosen answer is given in format $\{i\, \equiv 6mod5\}$

So is my answer same as given in text?
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R is a relation on the set of all functions from Z to Z.R = { (f, g) | for some C ∈ Z , for all x ∈ Z , f(x) - g(x) = C } is it Equivalence relation or not ?