.. This file is part of the OpenDSA eTextbook project. See
.. http://opendsa.org for more details.
.. Copyright (c) 2012-2020 by the OpenDSA Project Contributors, and
.. distributed under an MIT open source license.

.. avmetadata::
   :title: Relations Review with Programmed Instruction Framesets
   :author: Cliff Shaffer; Eunoh Cho; Mostafa Mohammed
   :institution: Virginia Tech
   :satisfies: relations
   :topic: Relations
   :requires: set notation
   :keyword: Set; Relation; Equivalence Class; Partial Order
   :naturallanguage: en
   :programminglanguage: N/A
   :description: Review materials on relations appropriate for a course in Data Structures and Algorithms or Formal Languages. Uses Programmed Instruction Framesets. 

Relations
=========

Relations
---------

Hopefully you found the material on sets in the last module fairly
simple, and maybe familiar from previous courses.
If you have had a discrete math class, than you are probably also
familiar with the concept of relations.
But unlike basic set notation, most people have a lot of trouble
understanding the concept of a relation (many overthink the idea), and
even more trouble with the different classifications.
So we will cover the basics in some detail, and follow up with some
practice exercises.

.. inlineav:: RelationsFS ff
   :links: AV/PIFLA/Background/RelationsFS.css
   :scripts:  DataStructures/PIFrames.js AV/PIFLA/Background/RelationsFS.js
   :output: show
   :keyword: Sets; Relations

.. avembed:: Exercises/Background/SetTFrelation.html ka
   :long_name: Relations Exercise
   :keyword: Sets; Relations
 
Equivalence Classes and Partial Orders
--------------------------------------

.. inlineav:: EquivFS ff
   :links: AV/PIFLA/Background/EquivFS.css
   :scripts:  DataStructures/PIFrames.js AV/PIFLA/Background/EquivFS.js
   :output: show
   :keyword: Sets; Relations; Equivalence Relation

.. avembed:: Exercises/Background/SetTFequivrel.html ka
   :long_name: Equivalence Exercise
   :keyword: Sets; Relations; Equivalence Relation

.. avembed:: Exercises/Background/SetTFpartialorder.html ka
   :long_name: PartialOrder Exercise
   :keyword: Sets; Relations; Partial Order