I'm reading the Lawvere and Schanuel's "Conceptual mathematics", and could't solve both (a) and (b) of Exercise 8.

[![enter image description here](https://i.stack.imgur.com/ZosNN.png)](https://i.stack.imgur.com/ZosNN.png)

What I understood is below.

In a category of graph, an object is a graph, and a map is from graph to graph.
Below image is a map $(f\_A, f\_D)$ of graph from $(X, Y, s, t)$ to $(X^{'}, Y^{'}, s^{'}, t^{'})$. In this map, $f\_D s = s^{'} f\_A$ and $f\_D t = t^{'} f\_A$ hold.

[![map of graph](https://i.stack.imgur.com/EbJRI.png)](https://i.stack.imgur.com/EbJRI.png)

Suppose in graph $G$, $x$ represent any arrows(edges) whose source is $b$, and $y$ represent any arrows(edges) whose target is $e$.
According to $f\_D s = s^{'} f\_A$, $f\_D t = t^{'} f\_A$, $f\_D(b)=0$, and $f\_D(e)=1$, I could show $s^{'}f\_A(x)=0$ and $t^{'}f\_A(y)=1$. So in graph $J$, $f\_A(x)$ is equal to the arrow from 0, and $f\_A(y)$ is equal to the arrow to 1.

Please give me advice to prove (a) and (b) of Exercise 8.