Let A = {2, 3, 4, 5, 6, 7, 8} and define a relation T on A as follows. For every x, y EA, x Ty 3|(x − y). Which of the following is the directed graph of T? 2 3 Co Се 2 2 о 5 2 7 8 3 (3) 10 3 6 2 5 3
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- (b) Let A = {1,2,3}. Consider the relation R on A given by R = {(1,2), (1,3), (2,1), (2,3), (3,2)} Draw the directed graph representing R. Is R transitive? Justify your answer.Define a relation R₂ on the set A = {0, 1, 2, 3) as follows. R₂ = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3)} (a) Which of the following is the directed graph of R₂? DO (b) Is R₂ reflexive, symmetric, transitive, or none of these? (Select all that apply.) R₂ is reflexive. R₂ is symmetric. R₂ is transitive. OR₂ is neither reflexive, symmetric, nor transitive. xDraw a directed graph for the relation R on the set {0, 1, 2, 3} given by 10. R = {(0, 1), (0, 2), (1, 2), (2, 2), (3, 1), (3, 3)}.
- 8) Let R = {(x, y) iff x∣ y} be a relation on set A ={1,5,6,7} Write the relation R in tabular or roster form. Find the matrix of a relation R. Draw digraph of the relation R. Find the indegree and out degree of the relation R. Compute the complement of relation R.Let A = {6, 8, 13, 15, 9, 16} and define a relation R on A as follows: xRy ⟺ 7 |(x – y) Draw a directed graph for R.Let A = {a, b, c, d} and define a relation R on A. The directed graph of the relation is shown here. Is the relation symmetric ? Explain why or why not.