I need some help with this task:
Given the function $f: \{1,2,3\} \to \mathbf{N}, f (1) = 1, f (2) = 3, f (3) = 2$.
a) Find the graph $\operatorname{graph}(f)$ of $f$.
b) By $f$, a relation is given on the set $\{1, 2, 3\}$. Examine these for reflexivity, symmetry, antisymmetry, and transitivity.
As far I as I understand it by talking about graph we are not talking about pictures visualising the function f but rather about the set
$$\operatorname{graph}(f):= \{(x,y) \in A \times B : y=f(x)\}$$
But how do I continue from that? Like so:
$$A = \{1,2,3\} \text{ and } B = \mathbf{N}$$
So $\operatorname{graph}(f) = \{(x,y) \in A \times B: y=f(x)\}$? It can't be that simple, right?
Any help is much appreciated :)