Question: Please prove this theorem: Theorem 31.14 (A nonempty closed subset of a finite group is a subgroup) If (S,) is a finite group and S

Please prove this theorem:

Please prove this theorem: Theorem 31.14 (A nonempty closed subset of a

Theorem 31.14 (A nonempty closed subset of a finite group is a subgroup) If (S,) is a finite group and S is any nonempty subset of S such that abS for all a,bS, then (S,) is a subgroup of (S,)

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