RTUComputer ScienceYr 2024 · Sem 42024

Q2Discrete Mathematics Structure

Question

2 marks

Define the properties of Partial Order Relation.

Answer

A Partial Order Relation is Reflexive, Antisymmetric, and Transitive.

A relation $R$ on a set $A$ is a partial order relation if it satisfies the following properties:

Reflexivity: $\forall a \in A, (a, a) \in R$ .
Antisymmetry: $\forall a, b \in A$ , if $(a, b) \in R$ and $(b, a) \in R$ , then $a = b$ .
Transitivity: $\forall a, b, c \in A$ , if $(a, b) \in R$ and $(b, c) \in R$ , then $(a, c) \in R$ .