Let S be a finite set with
Chapter 11, Problem 10(choose chapter or problem)
Let S be a finite set with |S| = n 2 and let R be a relation on S. For each element x S, let nx = |{y S : (x, y) R}|. Let f : S {1, 2, . . . , n} be a function defined by f(x) = nx for each x S. Prove that if R is an equivalence relation, then f is not bijective.
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