3. (40 points) Once upon a time a farmer went to a 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 rental a lxx1i . Iint criraing the river lw lxN . he farnKro'11 cally only hinnxlf and a single one of his purchases: the fox, the goose, or the bag of beans. If left unattended together, the fox would eat the goose, or the goose would eat the beans. Will the farmer be able to carry himself and his purchases to the far bank of the river, leaving each purchase intact? While you may easily find the answer to this problem online, we are interested in a method that solves this and similar river crossing puzzles. Show that you can model the problem with a FSM and then apply model checking concepts to solve it