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

Consider the equivalence relation on Z defined by the prescription that all positive numbers are equivalent, all negative numbers are equivalent, and 0 is only equivalent to itself. Let f ∶ Z → {a, b} be the function that maps all negative numbers to a and all 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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Expert Solution

Colby Messinger answered 1 year ago

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