Let A {a,b,c}, B = {d, e, f,g} and C = {1,2,3,4,5). Consider the following two relations R and S given as follows: R: A B given by R = {(a,d),(a, e), (b, e), (c,d), (c, e), (c,g) } S: B XC given by S = {(d, 1), (d, 2),(d,3), (f ,4),(g,1),(g,3), (9,5) } (a) State the zero-one matrix representation of the relation S. In this matrix representation, use the ordering of the elements of B and of C that is indicated in the above definition of B and C. (b) Write down the composition SR, stating the result as a set consisting of ordered pairs. (c) Consider the following directed graph G which is a graphical representation of a relation W on the set D = { 1,2,3,4}: 3 4 Describe explicitly which edges are introduced/removed in the following descriptions: (a) (b) Adding one new edge to G results in a graphical representation of a reflexive relation on D. Removing three of the edges from G results in a graphical representation of a symmetric relation on D. (c) Adding one new edge to G results in a graphical representation of a transitive relation on D