For the Man, Cabbage, Goat, Wolf problem:

a) List all the invalid states for this problem, that is, in which the goat is left alone with the cabbage, or the wolf is left alone with the goat.

b) Give the shortest sequence of steps that solves the MCGW problem.

c) Give the sequence of state representations that correspond to your solution starting with (E,E,E,E) and ending with (W,W,W,W).

d) There is an alternate means of representing states. Rather than a sequence representation, a set representation can be used.

In this representation, if an item is on the east side of the river, its symbol is in the set, and if on the west side, the symbol is not in the set as shown below, {M,C,G,W}all items on east side of river (start state) {C,W}cabbage and wolf on east side of river, man and goat on west side { }all items on the west side of the river (goal state) Give the sequence of states for your solution to the problem using this new state representation.