Ques-3-Show-that-Z-4-is-a-group-Hence-find-the-order-of-the-group-and-of-the-element-2-Z-4-if-it-exists-Ques-4-Prove-the-if-a-b-are-any-elements-of-a-group-G-then-the-e

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Question Number 193712 by Mastermind last updated on 18/Jun/23

$$\mathrm{Ques}.3$$$$\mathrm{Show}\mathrm{that}({\mathbb{Z}}_4,+)\mathrm{is}\mathrm{a}\mathrm{group}.\mathrm{Hence}$$$$\mathrm{find}\mathrm{the}\mathrm{order}\mathrm{of}\mathrm{the}\mathrm{group}\mathrm{and}\mathrm{of}\mathrm{the}$$$$\mathrm{element}2\in {\mathbb{Z}}_4,\mathrm{if}\mathrm{it}\mathrm{exists}.$$$$$$$$\mathrm{Ques}.4$$$$\mathrm{Prove}\mathrm{the}\mathrm{if}\mathrm{a},\mathrm{b}\mathrm{are}\mathrm{any}\mathrm{elements}\mathrm{of}\mathrm{a}$$$$\mathrm{group}(\mathrm{G},\ast ),\mathrm{then}\mathrm{the}\mathrm{equation}\mathrm{y}\ast \mathrm{a}=\mathrm{b}$$$$\mathrm{has}\mathrm{a}\mathrm{unique}\mathrm{solution}\mathrm{in}(\mathrm{G},\ast ).$$$$$$$$\mathrm{Help}!$$

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