A maximal element of a set is an element that is greater than or equal to all other elements in the set. In other words, there is no other element in the set that is larger than the maximal element.
A greatest element of a set is similar to a maximal element, but it is only defined in partially ordered sets. It is the element that is greater than or equal to all other elements in the set, but it may not exist in all sets.
A minimal element of a set is an element that is less than or equal to all other elements in the set. In other words, there is no other element in the set that is smaller than the minimal element.
A least element of a set is similar to a minimal element, but it is only defined in partially ordered sets. It is the element that is less than or equal to all other elements in the set, but it may not exist in all sets.
To determine these elements, you must first understand the order or relation that is defined for the set. For example, in a set of integers, the greatest element would be the largest integer in the set. In a set of real numbers, the maximal element would be the element closest to infinity. Once you understand the order, you can compare the elements in the set to find the maximal, greatest, minimal, and least elements.