Relations

Questions While Studying

What is a relation? It just relates to elements in a set A. Formal definition is that when you apply a relation to a set then that relation R is the set of $\mathbb{A} \text{x} \mathbb{A}$ where each element of A relates the other element of A.

Define what a reflexive relation is $xRx$ Define what an irreflexive relation is $x\not{R} x$ Define what a symmetric relation is $xRy \land yRx$ Define what an antisymmetric relation is $xRy \land y\not{R}x$ Define what a transitive relation is $xRy \land yRz \implies xRz$ What are some weird sets where S is transitive? (edge cases)

What are the four types of relations mentioned? Linear order, partial order, equivalence , and strict partial order. Linear order: transitive, antisymmetric, irreflexive, comparable Partial order: transitive, antisymmetric, reflexive Strict partial order: transitive, antisymmetric, irreflexive

See Also

1. [[discrete-math]]