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  3. consider the equivalence relation on z defined by

Consider the equivalence relation on Z defined by the prescription that all positive numbers are equivalent,...

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Advance Math

Consider the equivalence relation on Z defined by theprescription that all positive numbers are equivalent, all negativenumbers are equivalent, and 0 is only equivalent to itself. Let f ∶Z → {a, b} be the function that maps all negative numbers to a andall non-negative numbers to b. Does there exist a function F ∶ X/∼→{a, b} such that f = F ○ π? If so, describe it

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