Question

Define partial order and total order of relations

Answer 1

Solution:

A relation T on a set M is called a partial order relation when it satisfies the following properties:

1. It's reflexive: (x, x) is in T for every x in M.
2. It's antisymmetric: If (x, y) is in T and (y, x) is in T, then x = y.
3. It's transitive: If (x, y) is in T and (y, z) is in T, then (x, z) is in T.

A binary relation R on a non-empty set A is a total order if the relation is

• connex
• antisymmetric, and
• transitive.