Relations & Orderings

Reflexive Relation Condition

Irreflexive Relation Condition

Symmetric Relation Condition

Antisymmetric Relation Condition

Transitive Relation Condition

Linear Relation Condition

When is R on A an equivalence relation?

When is R on A a quasi ordering?

When is R on A a reflexive ordering/ irreflexive ordering?

What is condition for a reflexive/irreflexive ordering to be a linear ordering?

The relation must also be linear

Irreflexive Lexicographic Ordering Definition

Lexicographic Ordering for Reflexive Ordering

Equivalence Relation Examples

=, =(val)

Quasi-Ordering Examples

=>

( Partial ) Ordering Reflexive Examples

⊆, |=(val)

( Partial ) Ordering Irreflexive Examples

⊂

Linear Reflexive Ordering Examples

Greater or Equal / Smaller or Equal

Linear Irreflexive Ordering Examples

Greater / Smaller

Reflexive Ordering Extreme Elements ( Minimal,Maximal, Maximum, Minimum )

Irreflexive Ordering Extreme Elements ( Minimal,Maximal, Maximum, Minimum )

Upper / Lower Bounds for Reflexive Ordering