   Chapter 8.5, Problem 38ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
1 views

# Prove that a partially ordered set is totally ordered if, and only if, it is a chain.

To determine

To Prove:

A partially ordered set is totally ordered if, and only if, it is a chain.

Explanation

Given information:

A partially ordered set.

Concept used:

A subset B of A is called a chain if and only if the each pair of elements in B is comparable.

Proof:

Prove that if partially ordered set is totally ordered then it is a chain.

Let the partially ordered set be S equipped with the partial order relation _.

In this case the set S is totally ordered set with the partial order relation _ that means for every two elements a and b in the set S either a_b or b_a.

Write the definition of chain.

A subset B of A is called a chain if and only if the each pair of elements in B is comparable. In other words a_b or b_a.

Use this definition and also use the fact that every set is a subset of itself.

Since S is a subset of itself and it is totally ordered that means for each pair of elements in the set S either a_b or b_a

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 