Consider the “divides” relation defined on the set , where n is a nonnegative integer.
The “divides ” relation is a total order relation on given set:
If given set is reflexive, antisymmetric and transitive then the given set is called of partial order.
Is reflexive: suppose . Then .
Is antisymmetric: For suppose . Then there exist two integers such that .
Since and hence .
Since are two positive integers .
Is transitive: For suppose that
The Hasse diagram for this relation for .
Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!Get Started