Determine the relation is partially ordered, Mathematics

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Determine if the relation represented by the following Boolean matrix is partially ordered.

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Ans: Let the following relation R is defined on set A = {x, y, z}. To test if the relation R is partially ordered, we have to test if R is reflexive, anti symmetric and transitive.

Reflexivity: As all elements in the principal diagonal is '1', R is reflexive.

Anti Symmetry: In the following relation, we do not comprise any pairs (x, y) & (y, x) like that x ≠ y that is for (x, y) & (y, x) in R, x = y. So R is anti symmetric.

Transitivity: The relation is not transitive since for (y, x) & (x, z) in R, (y, z) is not in R. Hence R is not partially ordered.

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