the set X={1,2,3,5,30} with the partial order relation 'division' is
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Consider a relation R on a set S satisfying the following properties:
R is reflexive, i.e., xRx for every x ∈ S.
R is antisymmetric, i.e., if xRy and yRx, then x = y.
R is transitive, i.e., xRy and yRz, then xRz.
Then R is called a partial order relation, and the set S together with partial order is called a partially order set or POSET and is denoted by (S, ≤).
R is reflexive, i.e., xRx for every x ∈ S.
R is antisymmetric, i.e., if xRy and yRx, then x = y.
R is transitive, i.e., xRy and yRz, then xRz.
Then R is called a partial order relation, and the set S together with partial order is called a partially order set or POSET and is denoted by (S, ≤).
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