Sect 2c. Relations

CONCEPTS

  Relation, cartesian product, binary relation
  Composition, inverse
  Properties: reflexive, symmetric, transitive, antisymmetric
  Representation of binary relations
  Partial order, comparable, predecessor, successor, Hasse diagram
  Equivalence, equivalence class, quotient, partition
  Programming

NOTATION

SKILLS
  
  1. Identify concepts in a context
     E.g., tell whether a set is a relation
     E.g., tell whether some elements are related
  2. Tell properties of relations
     E.g., tell whether a relation is binary
     E.g., tell whether a given relation is symmetric or transitive or ...
  3. Determine relations given properties
     E.g., tell the composition of two relations
     E.g., construct the Hasse diagram of a partial order
     E.g., determine the partition induced by an equivalence
     E.g., tell whether two elements are equivalent or comparable
  
SOURCES

  *** Recommended ***   
  Tutorialspoint: Discrete Mathematics - Relations
  https://www.tutorialspoint.com/discrete_mathematics/discrete_mathematics_relations.htm

  *** Recommended ***
  Youtube: Discrete Math 1 by TheTrevTutor, videos 47-49
  https://www.youtube.com/playlist?list=PLDDGPdw7e6Ag1EIznZ-m-qXu4XX3A0cIz

  wikibooks: Discrete Mathematics/Functions and relations
  https://en.wikibooks.org/wiki/Discrete_Mathematics/Functions_and_relations

  *** Recommended ***   
  Lerma, sect 2.3

  ADS, sect 6.1-6.3 (lots of examples and exercises)

  Hammack, chap 11 (!!! lots of examples and exercises !!!)