Consider the following problem:

Once upon a time a farmer went to market and purchased a fox, a goose, and a bag of beans. On

his way home, the farmer came to the bank of a river and hired a boat. But in crossing the river by

boat, the farmer could carry only himself and a single one of his purchases $-$ the fox, the goose, or

the bag of the beans.

If left alone, the fox would eat the goose, and the goose would eat the beans.

The farmer's challenge was to carry himself and his purchases to the far bank of the river, leaving

each purchase intact. How could he do it$?$

Use state space search method to solve this problem. Let nodes represent states of the world and use j to

separate the banks. For example, the state where the farmer and the goose are on the starting bank and the

fox and beans on the far bank is represented as a state $($F$,$ g j f$,$ b$),$ where F is farmer, g is goose, f is fox, and

b is beans. The start state is $($F$,$ f$,$ g$,$ b j$).$

$($a$)$ Draw the WHOLE state space.

$($b$)$ Give the list of nodes visited and the solution using DFS$.$

$($c$)$ Give the list of nodes visited and the solution using BFS$.$