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.