Question

Determine Poset properties of the given relation.

Short answer

\(R\) is not a poset, as it is not reflexive.

Step-by-step solution

Given data

\(R\) is the relation, a related to \(b\) if a does not divide \(b\).

Concept used of partially ordered set

A relation\(R\)is a poset if and only if,\((x,x)\)is in\({\rm{R}}\)for all x (reflexivity)

\((x,y)\)and\((y,x)\)in R implies\(x = y\)(anti-symmetry),\((x,y)\)and\((y,z)\)in R implies\((x,z)\)is in\({\rm{R}}\)(transitivity).

Find  if the \(R\) is poset

\(R\) is not reflexive as a always divides a. \({\rm{R}}\) is not a poset, as it is not reflexive.