A partial order is defined as a relation on a set that is reflexive, antisymmetric, and transitive. A set equipped with a partial ordering is known as a partially ordered set (poset). An example poset is provided using the set {1, 2, 3} with a specific relation.

1. Lattice
BY Rohit Sharma

2. Parially Ordered Set
• A relation R on a set S is called a partial
order if it is reflexive, antisymmetric, and
transitive. A set S together with a partial
ordering R is called a partially ordered set, or
poset.
( , )
a b R

In a poset the notation a b
denotes that

3. Example (1)
Let S = {1, 2, 3} and
let R = {(1,1), (2,2), (3,3), (1,
2), (3,1), (3,2)}
1
2
3