1. Let A = {2, 3, 4, 5, 6, 7, 8) and R a relation over A. Draw the directed graph and the binary matrix of R, after realizing that xRy iff x-y = 3n for some n E Z.
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- Given the following matrix representation of a relation RR on the set A={a,b,c,d}A={a,b,c,d}, which of the following tuples is not in the relation?Given that T is a relation on the set {1, 2, 3, 4}, and the set of ordered pairs is: T = {(1, 1), (1, 2), (1, 4), (2, 1), (2, 3), (3, 2), (3, 3), (3, 4), (4, 1), (4, 3), (4, 4)}. Can you draw T as a directed graph? Can you show T as a matrix with elements that are zeros and ones? Is T reflexive? Can you explain why?Let M be the matrix representation of some relation R on set A. A has n elements. Thus, M would be n x n. How many 1's and O's will M have if R is a rooted (directed) tree?
- Let A = {2, 3, 4, 5, 6}, B = {11, 12, 13, 14, 15} and define the relation R from Ato B by aRb if a|b. Construct the matrix M corresponding to R.For the following relation on S = {1, 2, 3, 4, 5, 6}: p = {(1, 2), (1, 6), (2, 1), (3, 5), (4, 5), (6, 3), (6, 6)} Draw the directed graph and find the adjacency matrix.Consider the matrix representing a relation R on the set {x, y, z}. 0 1 0 1 0 1 1 0 1 List the pairs in this relation, where row/column 1 corresponds to x, row/column 2 corresponds to y, and row/column 3 corresponds to z.
- Suppose A is a bipartite graph that has color classes V and W. So if for all v∈V and w∈W, then d(v)≥d(w). Prove that A has a perfect matching of V into W.Draw a directed graph diagram for relation S on {0, 1, 2, 3,4}, where TSy iff x + y = 4Enter the smallest subgroup of M2(ℝ)× containing the matrix (−2 −1 3 1), as a set.
- Determine whether the set in P_2 is linearly independent. S={x^2 , +1, 2 - 1, 2}Find matrix A such that given set is Col A.Given the following adjacency matrix, A, for nodes a, b, c, and d, find the transitive closure of A. Is the result an equivalence relation, and why or why not? A = ⌈ 1 0 1 0 ⌉ | 0 1 1 0 | | 1 0 0 1 | ⌊ 1 1 0 0 ⌋