N = {1, 2, 3, ...},
N_{even} = {2,4,6,...} = \{2k \in N : k \in N\},
N_{odd} = {1,3,5, . . .} = \{2k - 1 \in N : k \in N\}.
Consider the function $f: N \to Z$ defined as
$f(n) = \frac{(-1)^n(2n - 1) + 1}{4}$.
(a) Show that $f : N_{even} \to N$ is bijective.
(b) Is it possible to find $A \subset Z$ such that $f : N_{odd} \to A$ is bijective? Justify your
answer.
(c) Is it possible to find $B \subset Z$ such that $f : N \to B$ is bijective? Justify your answer.
