a) Explain (step by step) how the Bellman-Ford algorithm can be used to solve the following difference constraints: x1x27x2x33x1x34 b) The longest path in a graph can be computed by negating the costs of all edges in the graph and then running the Floyd-Warshall algorithm. True or False? Explain: If it is True then give a proof. If it is False, then give a counterexample and explain what the algorithm returns. (c) Suppose that there are 3 students, {A,B,C}, and 4 graduation projects, {p,q,r,y}. Each student specifies a set of projects they would like to work on, and each supervisor of the project specifies a set of students whom they would like to work with: A:{p,q,r}B:{r,y}C:{q,r}p:{A,B,C}q:{C}r:{C,D}y:{A,B} Explain (step by step) how the Ford-Fulkerson algorithm can be used to assign projects to the maximum number of students, such that the following two conditions hold: there is no student matched to two different projects, and there is no project assigned to two different students