1. ## injection

$\displaystyle f:\emptyset\to Y$
is function f injective? as we know, it is, if:
$\displaystyle x,y \in \emptyset$
$\displaystyle f(x)=f(y)\Rightarrow x=y$
so left side is always false, because x and y cant be elements of empty set? and then f is always injective?

2. Yes, f is always injective. To make it clearer, consider this:

f is not injective iff $\displaystyle \exists x, y \in \emptyset \ s.t. \ x \neq y, f(x) = f(y)$. Obviously, this can't happen.