Mathematical Systems and Group Theory (figure out rule to complete table)

[jtayag0622]

Hi!
I just need help with this problem.


It's pretty hard for me. and also, I don't understand cancellation law like the one below:


Thanks for you help!

 

[Dr.Peterson]

I just need help with this problem.
View attachment 10244

It's pretty hard for me. and also, I don't understand cancellation law like the one below:
View attachment 10245

It looks like you cut off part of the problem that tells you what the operation is. Without some definition, how can you fill out the table?

Then, you'll have to tell us what you are having trouble with. Do you not know what each law means, or is it how to apply them? It will be best if you can show your work as far as you can get, so we can see where you need help. If you can do nothing, then you might show us an example you were given, so we can explain it. I'm not entirely sure how these ideas are being presented to you.

As for the cancellation law, you showed an example; were you also given a definition (that is, a statement of the law)? The basic idea is that if you ever get the same result when you multiply two different elements a and b by the same element, c, so that c*a = c*b, then you are violating this "law", which means it doesn't apply to this operation.

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[jtayag0622]

Hi,

Thank you so much. The instruction was I needed to discover the rule so I could fill in the table correctly. As for the cancellation law, I now understand it. Thanks a lot.

 

[Dr.Peterson]

Hi,

Thank you so much. The instruction was I needed to discover the rule so I could fill in the table correctly. As for the cancellation law, I now understand it. Thanks a lot.

My guess is that the table is supposed to represent the GCD: a*b = GCD(a,b). But you can't be sure of that just from parts of a table, unless you are told something else about it (such as some properties of the operation); any way you fill the table with values from the given set, it will represent some operation! That's why I was hoping they said something more than I can see.