Concept
What are the reflexive, symmetric, antisymmetric, and transitive properties of the endorelation T?
Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk / Chapter 1
"O be an endorelation on T , defined as follows: { (Kirk, Scotty), (Spock, Scotty), (Kirk, Spock), (Scotty, Spock) }. Is T reflexive? No, since it doesn’t have any of the elements of T appearing with them- selves. 7. Is T symmetric? No, since it contains (Kirk, Scotty) but not (Scotty, Kirk). 8. Is T antisymmetric? No, since it contains (Spock, Scotty) and also (Scotty, Spock).\n\n52 CHAPTER 3. RELATIONS 9. Is T transitive? Yes, since for every ( x, y ) and ( y, z ) present, the corresponding ( x, z ) is also present. (The only example that fits this is x =Kirk, y=Spock, z=Scotty, and the required ordered pair is indeed present.)"
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