Let R be the relation “is a prerequisite for” from the set of CSC courses at UNCW. We have
121 R 241
121 R 221
241 R 332
221 R 332
332 R 342
332 R 337
332 R 360
and so forth. Is R reflexive? (Vacuously by definition.) R is obviously transitive. Is R symmetric? To answer this, note that there are no courses x, y such that x R y Ů y R x except that if this were so, x and y would be the same course. We can however, say that R is anti-symmetric. In this example 121, 221, 241, 332, 337, 342, and 360 are partially ordered, that is R is reflexive, anti-symmetric and transitive (RAT). That is to say, they form a poset (partially ordered set). In the drawing below the transitive relations that complete the link from a to c when a R b and b R c, i.e. those implied by the transitive property, are left out for clarity. Additionally reflexive loops implied but not drawn.