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posted by  ttrain on 8/25/2008 6:36:07 PM  |  status: Live  

Discrete Math - Algebraic Structures and Techniques

Course Textbook Chapter Problem
Discrete Math Disrete Mathematics, 2nd ed., James L. Hein, ISBN# 0-7637-2210-3 10.1 4b
Question Details:
Given a binary operation on a finite set in table form, describe an easy way to detect whether the binary operation has the listed property:
 
b)  The operation is commutative
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posted by Galois on 8/29/2008 3:50:00 AM  |  status: Live
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ttrain's comment:
"Thanks so much. If you have a chance, take a look at some of the other questions I've posted recently."
Response Details:
Now, observe thatthis operation is commutative in S:
Observe that for any a, b, the sum a+b modulo3 is provided in the table.
for example 2 +3 2 = 4(modulo 3) =1.
∴we have  a +3 b = b +3 a, for all a, b in {0, 1, 2}. 
 
 
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