CS 173, Fall 2015: Skills list for fourth examlet

• Relations
  • Define a relation R on a set A, using the notation xRy.
  • Represent a relation as a directed graph.
  • Define reflexive, irreflexive, symmetric, anti-symmetric, transitive. For any of these problems, determine if a specific relation has the property. In particular, be sure you know
    • When one of these properties is vacuously true (e.g. what are the properties of a relation with no arrows at all?)
    • How to recognize or construct a relation that is neither irreflexive nor reflexive, or neither symmetric nor antisymmetric.
  • Know what it means for two elements in a relation to be comparable.
  • Define equivalence relation, partial order, strict partial order, linear order.
• Equivalence Classes
  • For an equivalence relation R and an element x, define the equivalence class [x].
  • For a specific value of x, determine what's in [x]
  • List or describe all of R's equivalence classes.
• Relation proofs
  • Prove that a relation does or doesn't have one of the standard properties (reflexive, irreflexive, symmetric, anti-symmetric, transitive).
  • Prove that a relation is, or isn't, an equivalence relation, an partial order, a strict partial order, or linear order.