Suppose we are given a directed graph G with n vertices, and let M be the n n adjacency matrix corresponding to G (a) Let the product of M with itself (M2) be defined, for 1 i,jn, as follows: where is the logical or operator and O is the logical and operator. Given this definition, what does M2(i,j)-l imply about the vertices i and J? What if M2(i,j) = 0? b) Now suppose that G is weighted and assume the following . for 1 .for 1 . for 1 i n, M(i, i) = 0 i,j n, M(i,j)- weight(i,j) if (i,j)E E i,j n, M(i, j) = oo if (i,j) E Also let M2(i,j) be defined, for 1 i,jS n, as follows: MP(i, j)-min(M(i, l) + M(Lj), . . . , 1(i, n) + M(n)]. If M2(i, j)-k. what may we conclude about the relationship between vertices i and j