   Chapter 8.3, Problem 44ES ### 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

# Let A = Z + × Z + . Define a relation R on A as follows: For every (a,b) and (c,d) in A, ( a , b ) R ( c , d )     ⇔   a + d = c + b . Prove that R is reflexive . Prove that R is symmeteic. Prove that R is transitive. List five elements in [ ( 1 , 1 ) ] . List five elements in [ ( 3 , 1 ) ] List five elements in [ ( 1 , 2 ) ] . Describe the distinct equivalence classes of R.

To determine

(a)

To prove that the given relation R is reflexive.

Explanation

Given information:

Let A=Z+×Z+. Define a relation R on A as follows: For all ( a, b ) and ( c, d ) in A ,

(a,b) R (c,d)        a+d=c+b.

Proof:

A=Z×ZR={(( a,b),( c,d))A×A|a+d

To determine

(b)

To prove:

Prove that R is symmetric.

To determine

(c)

To prove:

Prove that R is transitive.

To determine

(d)

List five elements in [(1,1)].

To determine

(e)

List five elements in [(3,1)].

To determine

(f)

List five elements in [(1,2)].

To determine

(g)

Describe the distinct equivalence classes of R.

### 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 