Solve Abstract Algebra Problems with Expert Help | Abstract Algebra Assistance"

[elle]

Abstract algebra help please!

I'm not sure if I've posted in the correct forum but I would like some help with the following question:

http://i12.tinypic.com/33mlik6.jpg"

I've to complete this table but I am unsure of how to do the very first step which is to fnd wv.

I am learning this from a book and this is one of the given exercises however it doesn't provide a solution so I am really stuck. Hope someone can help!

I know the associative law is:

a * ( b * c ) = (a * b) * c

(but I am unsure on how to apply this to my question. Can anyone start me off?)



thanks very much!

 

[radou]

Well, write down the facts you know from the table, for example w*x = z. Combine all these to obtain the value of w*v. In general, the associative law states that you can insert and delete brackets how you like.

 

[HallsofIvy]

You want w*v and the hint is to use the associative law: okay, it must be something like w*( ) where the ( ) is a product of two elements that give v: according to your table, what product gives a result of v?

 

[elle]

Okay thanks guys

I have got:

w*v =

w*(x*y) = w*(x*y)
= z*y
= u

Is that right? So w* v = u?

The next part of the question is to deduce the identity element so:

z*y = y*z = z? So the identity element is y?

 

[elle]

Hi again,

Could someone help me with this again? Very sorry to be a pain...I'm just so confused

I managed to deduce that the identity is u not y as I stated above. And my next step is to fill in the w row and z column but I don't know where to start. For example how can I find w*w?? Do I use the associative law again?

http://i12.tinypic.com/2guxmz8.jpg


Thanks in advance!