Solution Found!

(Socks–Shoes Property) Draw an analogy between the

Chapter 2, Problem 24E

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

(Socks–Shoes Property) Draw an analogy between the statement (ab)–1 = b–1 a–1 and the act of putting on and taking off your socks and shoes. Find distinct nonidentity elements a and b from a non-Abelian group such that (ab)–1 = a–1 b–1. Find an example that shows that in a group, it is possible to have (ab)–2 ? b–2 a–2. What would be an appropriate name for the group property (abc)–1 = c–1 b–1 a–1?

Questions & Answers

QUESTION:

(Socks–Shoes Property) Draw an analogy between the statement (ab)–1 = b–1 a–1 and the act of putting on and taking off your socks and shoes. Find distinct nonidentity elements a and b from a non-Abelian group such that (ab)–1 = a–1 b–1. Find an example that shows that in a group, it is possible to have (ab)–2 ? b–2 a–2. What would be an appropriate name for the group property (abc)–1 = c–1 b–1 a–1?

ANSWER:

Step 1 of 4

Sock- Shoe Property: This property is a direct analogy from real life to mathematical manipulations. If one thinks of  as putting on socks,  as putting on shoes, , as taking off socks, and  as taking off shoes, the theorem demonstrates the order in which one must perform these actions.

So, here  represents the action as: Putting on socks followed by putting on shoes.

So, the term  represents the action as: Putting off shoes followed by putting off socks.

Also, the term  represents the action as: Putting off socks followed by putting off shoes.

But you cannot put off socks before putting off shoes. So, for Sock-Shoe property  is not true. So, .

 

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