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Let f: Z6 --> Z2 X Z3 be the function given by f([a]6) = ([a]2,[a]3). (a)...

Let f: Z6 --> Z2 X Z3 be the function given by f([a]6) = ([a]2,[a]3). (a) Show that f is well-defined; that is, show that if [a]6=[b]6, then f([a]6) = f([b]6). (b) Prove that f is an isomorphism.

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