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Define partial order and total order of relations

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Solution:

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

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

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