1. (10 Points) Draw the graph represented by each adjacenty matrix with vertices a, b, c, d, e 0101 1 10101 A = 01201 0 0 0 02 1 1 1202. (10 Points) Draw the graph represented by the incidence matrix with vertices: v1, V2, v3, V4, 05, and edges: e1, e2, e3, e4, e5, e6, e7 1110000 0011 100 A = 0000010 1101000 00 0 01 10 3. (10 Points) Write the relation R from X to X relative to the ordering X: a, b, c, d given by the 1000 01 10 matrix, as a set of ordered pairs. A = 01 10 00014. (20 Points) Let R, be a relation from X = {1, 2, 3} to Y = {x, y } defined by R1 = { (1, x), (2, y), (3, x), (3, y) }; and let R2 be the relation from Y to Z = {a, b, c} defined by R2 = {(x, a), (x, b), (y, b), (b, z) } ; find (a) The matrix A, of the relation R1 (relative to the given orderings). (b) The matrix A2 of the relation R2 (relative to the given orderings). (c) The matrix AlA2. (d) Use the result of part (c) to find the relation R2 0 R1. 35. (20 Points) Write the relation R from X: w, x, y, z 1010 0 0 0 0 to Y: a, b, c, d, given by the matrix, A = 1010 0 0 01 as a set of ordered pairs and decide whether the relation is reflexive, symmetric, transitive, and/ or equivalence relation