A partially ordered set (or poset) is a mathematical structure consisting of a set of elements along with a binary relation that describes how these elements can be compared. In a poset, not all pairs of elements need to be comparable; that is, for some elements, neither can be said to be less than or greater than the other. The relation must be reflexive, antisymmetric, and transitive, which means each element is comparable to itself, if one element is less than another, the reverse is not true, and if one element is less than a second, and the second is less than a third, then the first is less than the third. Posets are commonly used in various fields, including computer science, where they can represent hierarchies or dependencies, such as in task scheduling or data organization. A familiar example of a poset is the set of subsets of a given set, ordered by inclusion. In this case, one subset is considered less