1. Let R be the relation on A = {1, 2, 3, 4, 5} given by R ={(1, 1),(1, 3),(2, 2),(2, 4),(2, 5),(3, 1),(3, 3),(4, 2),(4, 4),(4,5),(5, 2),(5, 4),(5, 5)}.
(a) Draw the digraph which represents R.
(b) Give the 0 -1 matrix of R with respect to the naturalordering.
(c) Which of the five properties (reflexive, irreflexive,symmetric, antisymmetric, transitive) does R have? Give a briefreason why or why not each property holds.
2. Let A = {1, 2, 3, 4}, B = {?, ?, ?}, and C = {x, y, z}.Further suppose S = {(1, ?),(2, ?),(2, ?),(3, ?),(3, ?)} and R ={(?, x),(?, y),(?, z)}.
(a) Compute the composition relation R ? S. Hint: It may behelpful to draw bipartite graphs.
(b) Is the relation R ? S a function from A to B? Why or whynot?
