Basic Definition.

1. y R x means y is related to x through a relation R.

2.x R y means x is related to y through a relation R.


Some Definitions:

1. Upper Bound:

An elements x  such that all the elements of set or poset  'A'are related. ie. 

y R x :  ∀ y ∈ A and x ∈ A

x is called uppar bound.


2. Lower bound :

An element y is called lower bound if y R x  : ∀ x ∈ A and y ∈ A. 


3. Minimal Elements:

Informally, x is called a minimal element if no element is related to x.

It is present at a lower level.

4. Maximal Elements:

  1. Informally, x is called maximal elements if x is not related to any other elements.
  2. It is not compulsory that we always get unique maximal and minimal elements. We can have more than one maximal and minimal elements.



Contributor's Info