Which of the following relations are functions from $A$ to itself?

Question

If $A=\{1,2,3,4\}$, then which of the following are functions from $A$ to itself?

I. $f_1=\{(x,y) \mid x+y=5\}$
II. $f_2=\{(x,y) \mid y<x\}$

I haven't got an idea of this question and I need some hint.

Answer 1

Certainly the answer is $I$ because the condition for a relation $f$ to be function is that for every $y$ there is only one $x$ such that $(x,y)\in f$. In case$II$ we can have more than 0ne $x$ for example for $y=4$.