Hint for Section 10.2 Question 3

3. The ordered pairs in the relation R were found in question 8 of the previous section.

R = { (1,1), (4, 4), (7, 7), (10, 10), (1, 4), (4, 1), (1, 7), (7, 1), (1, 10), (10, 1), (4, 7), (7, 4), (4, 10), (10, 4), (7, 10), (10, 7),
(2, 2), (5, 5), (8, 8), (2, 5), (5, 2), (2, 8), (8, 2), (5, 8), (8, 5),
(3, 3), (6, 6), (9, 9), (3, 6), (6, 3), (3, 9), (9, 3), (6, 9), (9, 6) }

Your graph should have ten vertices and once you draw the edges, the graph should have three components.

Recall that if a relation R on a set A is specified as a directed graph, then R is:

• reflexive if, and only if, there is a loop at each vertex of the graph.
• symmetric if, and only if, whenever the directed edge (u, v) is in the graph, then the directed edge (v, u) is also in the graph.
• transitive if, and only if, whenever the directed edges (u, w) and (w, v) are in the graph, then the directed edge (u, v) is also in the graph.  

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