Question

Describe Partially Ordered Set

Answer 1

As Partial order defines a notion of comparison.

Two elements $xandy$ may stand in any of four mutually exclusive relationships to each other:

either$x<y,orx=y,orx>y,orxandy$ are incomparable. A set with a partial order is called a partially ordered set (also called a poset).

For example, The set N of natural numbers forms a poset under the relation '$\le$' because firstly $x\le x$, secondly, if$x\le yandy\le x$, then we have

$x=yandlastlyifx\le yandy\le z,itimpliesx\le zforallx,y,z\in N.$