a) Let A={1,2,3} B = {a,b,c,d) and C= {x, y, z, w). Suppose R and S are relations from A to B and from B to C respectively defined by R= {(1, a),(2, a), (2.c), (2, d), (3, b)} and S = {(a,x),(a, z), (c, w),(d, y)}. i. Draw an arrow diagram to represent the relation RS (2 marks) Show that the product of the matrix representation of R and S has the same representation as the matrix RS (4 marks) iii. Find the domain and range of RS (2 marks) b) Let S = {1,2,...9) and R be a relation on S defined by (a,b) = (c,d) if and only if a+d=b+c. i. Show that is an equivalence relation ii. Find the equivalence class of [2,5] c) Use Venn diagrams to determine the validity of the following arguments S: Some innocent people go to Jail S: Mary is innocent S, :All people in jail are bad people Conclusion: Mary is not a bad person. (6 marks) (2 marks) (4 marks)