Consider the set S of rational numbers whose denominators are even when written in lowest terms....

 

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Consider the set S of rational numbers whose denominators are even when written in lowest terms. So [3 -1 11 5 -7 S = 8 6 24 12 10 (a). Find a formula for an injective function f : N→ S. (b). Prove that your function f from part (a) is 1-to-1. (c). Does a bijection from N+ S exist? Briefly explain. Consider the set S of rational numbers whose denominators are even when written in lowest terms. So [3 -1 11 5 -7 S = 8 6 24 12 10 (a). Find a formula for an injective function f : N→ S. (b). Prove that your function f from part (a) is 1-to-1. (c). Does a bijection from N+ S exist? Briefly explain.