# What does it mean for a relation is a partial order relation?

What does it mean for a relation is a partial order relation?

## Solutions

##### Expert Solution

It means that the relation is reflexive, antisymmetric, and transitive.

Definition : Let R be a relation defined on a set A. R is a partial order relation if and only if R is reflexive, antisymmetric and transitive.

## Related Solutions

##### Determine if the binary relation <= is a partial order on A in the following cases:...
Determine if the binary relation <= is a partial order on A in the following cases: (a) A = N × N and (a1, b1) (a2, b2) ⇔ a1 <= a2 for (a1, b1),(a2, b2) ∈ A (b) X = {1, 2, 3, 4}, A = P(X) and a <= b ⇔ #a <= #b for a, b ∈ A (Here #a denotes the number of elements in the set a) (c) A = N and a <= b ⇔...
##### What does it mean for a relation to be left-definite?
What does it mean for a relation to be left-definite?
##### What does Public Relations mean? (in relation to marketing)
What does Public Relations mean? (in relation to marketing)
##### What does “education” mean for Wollstonecraft, and what role does it play in relation to gender?
What does “education” mean for Wollstonecraft, and what role does it play in relation to gender?
##### What does "derivability of relation" mean when it comes to relational databases?
What does "derivability of relation" mean when it comes to relational databases?
##### What does a stop order to sell at $2 mean? When might it be used? What does a limit order to sell at$2 mean?
What does a stop order to sell at $2 mean? When might it be used? What does a limit order to sell at$2 mean?
##### What does the term “management’s financial statement assertions” mean in relation to an audit? What are...
What does the term “management’s financial statement assertions” mean in relation to an audit? What are the different types of assertions and what is being asserted? Why is it necessary to understand the assertions when auditing?
##### CNS Immunity a. What does the term “immune privileged” mean in relation to the CNS? Be...
CNS Immunity a. What does the term “immune privileged” mean in relation to the CNS? Be sure to note which structure is responsible for the CNS being “immune privileged,” and how it works b. What are the immune cells of the CNS and their functions? c. What branch of the immune system is absent from the healthy CNS?
##### Problem 4.9.4 (10) In Section 2.10 we proved that every partial order is the “path-below” relation...
Problem 4.9.4 (10) In Section 2.10 we proved that every partial order is the “path-below” relation of a graph called a Hasse diagram. How does the Hasse diagram relate to the graph of the partial order itself? Present the proof of the Hasse Diagram Theorem using mathematical induction.
##### What does it mean that the style sheets are cascading? What is the order of priority...
What does it mean that the style sheets are cascading? What is the order of priority of CSS? List 5 things you can do with CSS, which cannot be done easily in HTML.