1. For each of the following functions, determine whether the function is
injective, surjective, both (bijective), or neither. Briefly explain your
answer. (40pt)
(a) $f : \mathbb{Z}^+ \to \mathbb{Q}^+$, $f(x) = 1/x$
(b) $f : \mathcal{P}(\mathbb{R}) \times \mathcal{P}(\mathbb{R}) \to \mathcal{P}(\mathbb{R})$, $f(A, B) = A - B$
(c) $f : \mathcal{P}(\mathbb{Z}) \to \mathbb{Z}$, $f(A) = |A|$
(d) $f : \mathcal{P}(\mathbb{Z}) \to \mathcal{P}(\mathcal{P}(\mathbb{Z}))$, $f(A) = \mathcal{P}(A)$
(e) $f : \mathbb{N} \to \mathbb{Z}$, $f(x) = (-1)^{\lfloor x/2 \rfloor}$
