Solution Found!

Define a relation ~ on JR bya ~ b iff lal = Ibl.(a) Prove that ~ is an equivalence

Chapter 9, Problem 9.7

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

Define a relation ~ on JR bya ~ b iff lal = Ibl.(a) Prove that ~ is an equivalence relation on JR. State clearly the properties of the relation =on JR that are used in the proof.(b) Give a complete set of equivalence class representatives.

Questions & Answers

QUESTION:

Define a relation ~ on JR bya ~ b iff lal = Ibl.(a) Prove that ~ is an equivalence relation on JR. State clearly the properties of the relation =on JR that are used in the proof.(b) Give a complete set of equivalence class representatives.

ANSWER:

Step 1 of 3

Consider the on  defined by  if and only if .

(a)

As per the reflexive property of  on , it is known that  for all  which gives  for all .

Therefore,  for all  and therefore,  is reflexive.

If  then . As per the symmetric property of  on ,  gives  which also gives  and therefore,  is symmetric.

 

Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back