CS 173, Fall 2014: Skills list for fourth examlet
- 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,
- 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,
- Prove that a relation is, or isn't, an equivalence relation, an
partial order, a strict partial order, or linear order.