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Question Number 192095 by Mastermind last updated on 07/May/23

$$\mathrm{Prove}\mathrm{a}\mathrm{non}-\mathrm{empty}\mathrm{set}\mathrm{S}\mathrm{of}\mathrm{a}\mathrm{group}$$$$\mathrm{G}\mathrm{wrt}\mathrm{binary}\mathrm{operation}\ast \mathrm{is}\mathrm{a}\mathrm{sub}-$$$$\mathrm{group}\mathrm{of}\mathrm{G}.\mathrm{Iff}$$$$1)\mathrm{a},\mathrm{b}\in \mathrm{S}\Rightarrow \mathrm{a}\ast \mathrm{b}\in \mathrm{S}$$$$2)\mathrm{a}\in \mathrm{S}\Rightarrow {\mathrm{a}}^{-1}\in \mathrm{S}.$$$$$$$$$$$$\mathrm{Hello}$$

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