2.7 Partial order relations 1. Partially ordered sets Definition 2.21: A relation on a set A is called a partial order if R is reflexive, antisymmetric, and transitive. The set A together with the partial order R is called a partially ordered set, or simply a poset and we will denote this poset by(A, R). And the notation asb denoted that (a, bER. Note that the symbol s is used to denote the relation in any poset, not just the " lessthan or equals relation The notation a< b denotes that a≤ b but a≠b.2.7 Partial order relations 1.Partially ordered sets Definition 2.21: A relation R on a set A is called a partial order if R is reflexive, antisymmetric, and transitive. The set A together with the partial order R is called a partially ordered set, or simply a poset, and we will denote this poset by (A,R). And the notation a≼b denoteds that (a,b)R. Note that the symbol ≼ is used to denote the relation in any poset, not just the “lessthan or equals” relation. The notation a≺b denotes that a≼b but ab