Problem 5. Recall the EXACT SET COVER problem: You are given a universal set U of elements and a collection W of subsets of U. The object is to find a subcollection Y of W such that every element of U is in exactly one set in Y. For instance, suppose that U is the set {a,b,c,d,e,f,g,h,i} and that W is the following collection: W1 = {a,d,f,h}, W2 = {b,e,g} W3 = {e,g}, W4= {d,e,i} W5 = {b,d,f,h}, W6 = {a,c,i} W7 = {c,d,e}, W8 = {b,c,f} Then one solution would be Y={W3,W5,W6}. 6 of 9 (a) Describe a state space for the general version of this problem. You should specify (a) what are the states; (b) what are the actions; (c) what is the start state; (d) what is the goal state? (b) Show the part of the state space generated by a depth-first search for the given exam- ple. Problem 5. Recall the EXACT SET COVER problem: You are given a universal set U of elements and a collection W of subsets of U. The object is to find a subcollection Y of W such that every element of U is in exactly one set in Y. For instance, suppose that U is the set {a,b,c,d,e,f,g,h,i} and that W is the following collection: W1 = {a,d,f,h}, W2 = {b,e,g} W3 = {e,g}, W4= {d,e,i} W5 = {b,d,f,h}, W6 = {a,c,i} W7 = {c,d,e}, W8 = {b,c,f} Then one solution would be Y={W3,W5,W6}. 6 of 9 (a) Describe a state space for the general version of this problem. You should specify (a) what are the states; (b) what are the actions; (c) what is the start state; (d) what is the goal state? (b) Show the part of the state space generated by a depth-first search for the given exam- ple