every poset is toset is true ?
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In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary relation indicating that, for certain pairs of elements in the set, one of the elements precedes the other in the ordering. The relation itself is called a "partial order." The word partial in the names "partial order" and "partially ordered set" is used as an indication that not every pair of elements needs to be comparable. That is, there may be pairs of elements for which neither element precedes the other in the poset. Partial orders thus generalize total orders, in which every pair is comparable.
The Hasse diagram of the set of all subsets of a three-element set {x, y, z}, ordered by inclusion. Distinct sets on the same horizontal level are incomparable with each other. Some other pairs, such as {x} and {y, z}, are also incomparable.
Formally, a partial order is any binary relation that is reflexive (each element is comparable to itself), antisymmetric (no two different elements precede each other), and transitive (the start of a chain of precedence relations must precede the end of the chain).
One familiar example of a partially ordered set is a collection of people ordered by genealogical descendancy. Some pairs of people bear the descendant-ancestor relationship, but other pairs of people are incomparable, with neither being a descendant of the other.
A poset can be visualized through its Hasse diagram, which depicts the ordering relation.
Answer:
a poset can be visualized through it hasse diagram which depicts the ordering relation
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