Let S be a non-empty set (finite or otherwise) and Σ the group
of permutations on...
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Let S be a non-empty set (finite or otherwise) and Σ the groupof permutations on S. Suppose ∼ is an equivalence relation on S.Prove (a) {Ï âˆˆ Σ : x ∼ Ï(x) (∀x ∈ S)} is a subgroup of Σ. (b) Theelements Ï âˆˆ Σ for which, for every x and y in S, Ï(x) ∼ Ï(y) ifand only if x ∼ y is a subgroup of Σ.
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