Define a relation R on R, the set of all real numbers as follows: For every
Is R a partial order relation? Prove or give a counterexample.
Whether is a partial order relation or not.
Consider a relation on the real number set as follows.
. For all .
A relation that is reflexive, antisymmetric, and transitive is called a partial order.
Objective is to identify whether the relation is partial order relation or not.
A relation on the set is a partial order relation if is reflexive, antisymmetric, and transitive.
A relation on the set is antisymmetric if for all , if then .
Here, the relation defined on a real number set is not a partial order relation since is not antisymmetric.