Intro to Relations in Discrete Math (and Ways to Represent Them)

Relations represent associations between elements of sets. If we're talking about just two sets, then a relation is a subset of the ordered pairs of the Cartesian product, AxB. Typically, relations are across two sets or from one set to the same set, but relations across n-tuples are also possible. Relations can also be modeled using directed graphs or matrices.

Timestamps
00:00 | Intro
00:28 | Review of Cartesian Product
02:02 | Relation as a Subset of Cartesian Product
03:23 | Rock, Paper, Scissors Example
05:28 | Relation Notation
06:41 | Cardinality of Relations
07:39 | Example of a Relation Across Two Sets
09:42 | Example of a Relation Across Two Lists/Tables
11:41 | Relations Across N-Tuples
13:18 | Relations Across a Single Set
15:06 | Domain of a Relation
16:05 | Range of a Relation
16:50 | The Relative Set, R(x0)
17:48 | Modeling Relations with Directed Graph
20:22 | Defining In-Degree and Out-Degree
22:15 | Modeling Relations with Matrix
24:39 | Domain, Range, and Relative Set, Example 1
27:09 | Directed Graph and Matrix, Example 1
29:08 | In-Degree and Out-Degree, Example 1
30:34 | Domain, Range, and Relative Set, Example 2
32:25 | Directed Graph and Matrix, Example 2

Hashtags
#relation #cartesian #graph