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Problem 5. Letf: Z+Zbyn -n. Let D, E S Z denote the sets of odd and even integers, respectively. (a) Prove that fD CE, where
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f: Z-Z 1 D odd integers f(n) = nn. I even integers @) To show : f(D) SE. Let MED. :: m = 2k+1 for some kEZ. : f(m) = 2k+1)-(2b fil R f(x) = x + 2x +1 = (x+1) (9) Note that f(-3)= (-3+1)= (-2) = 4 and f(1) = (1+1) = 2 = 4. Thus f(-3) = 4= f(1) but & -As pr rules, I have solved first four parts.

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