Question: 2. For a permutation p: X X, let p denote the permutation arising by a k-fold composition of p, i.e., p = p and p

2. For a permutation p: X X, let p denote the permutation arising by a k-fold composition of p, i.e., p = p and p = po pk-1. Define a relation on the set X as follows: i j if and only if there exists a k 1 such that pk (i) = j. Prove that is an equivalence relation on X, and that its classes are the cycles of p. iyi DK= D/ DK-)

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