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