Let A = {1,2,3,4}, B = {2,3,4,5}, and C = {2,4,6,8,10}. Suppose R is a 3-ary relation that is defined by the following rule: (a,b,c) is an element of R provided that a + 1 = b and b | c (meaning that b divides c with a remainder of zero), and where a ∈ A, b ∈ B, and c ∈ What triples are in the 3-ary relation R?

A4. a. Draw a Digraph represented by the adjacency matrix 1 1 1 1 1 1 1 b. Consider the recurrent relationA, = 2An-1 + 3An-2, where n 2 2 and A = 1, A, = 2. Compute the next 4 terms (A2, A3, A4, A5) of the relation.

11. Let C= {O, 1, 2) and D = (2, 4, 6, 8) and define a relation R from A to B as follows: For all (x, y) E AXB, %3D %3D y+2 (x, y) e R means that is an integer. a. Is 1 R 2? Is 2 R 8? Is (1, 8) e R? Is (2, 6) e R ? b. Write R as a set of ordered pairs. c. Write the domain and co-domain of R. d. Draw an arrow diagram for R.