Properties of relations
| Lecture #2: Review of Relevant Mathematics |
Properties of relations  | Reflexive R is reflexive iff (a,a) Î R for all a Î dom(R) |
| Lecture #2: Review of Relevant Mathematics |
Properties of relations  | Reflexive |
| | Symmetric R is symmetric iff whenever (a,b) Î R then (b,a) Î R for all a,b Î dom(R) |
| Lecture #2: Review of Relevant Mathematics |
Properties of relations | | Reflexive |
| | Symmetric |
| | Anti-symmetric R is anti-symmetric iff whenever (a,b) Î R then not (b,a) Î R for all a,b Î dom(R) |
| Lecture #2: Review of Relevant Mathematics |
Properties of relations | | Reflexive |
| | Symmetric |
| | Anti-symmetric |
| | Transitive R is transitive iff whenever (a,b) Î R and (b,c) Î R then (a,c) Î R for all a,b,c Î dom(R) |
| Lecture #2: Review of Relevant Mathematics |
Properties of relations | | Reflexive |
| | Symmetric |
| | Anti-symmetric |
| | Transitive |
| | Equivalence relations an equivalence relation is a relation which is reflexive, symmetric and transitive |
| Lecture #2: Review of Relevant Mathematics |
Properties of relations | | Reflexive |
| | Symmetric |
| | Anti-symmetric |
| | Transitive |
| | Equivalence relations |
| | Partial orders a partial order is a relation which is anti-symmetric and transitive |
| Lecture #2: Review of Relevant Mathematics |
Properties of relations | | Reflexive |
| | Symmetric |
| | Anti-symmetric |
| | Transitive |
| | Equivalence relations |
| | Partial orders |
| | Total orders if every pair of elements in a partially-ordered set is comparable under the partial order, we say that it is totally ordered |