# CS 173, Fall 2014: 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.