Q on associative binary operation

[Tim May]

On Thursday, August 28, 2003, at 12:14  AM, Sarad AV wrote:

> hi,
>
> Table shown is completed to define 'associative'
> binary operation * on S={a,b,c,d}.
>
> *|a|b|c|d
> ---------
> a|a|b|c|d
> ---------
> b|b|a|c|d
> ---------
> c|c|d|c|d
> ---------
> d|d|c|c|d
>
>
> The operation * is associative iff (a*b)*c=a*(b*c) for
> all a,b,c element of set S.
>
> So can (a*d)*d=a*(d*d)=d considered as associative
> over * for this case as per definition?
>

This looks like a homework assignment for a class.

If a, b, c, and d are all arbitrary symbols, most substitutions (such 
as a = 2, b = 5, etc.) certainly will _not_ give (a*d)*d=a*(d*d)=d as a 
true statement. Only special values of a and d will make that true. 
(For example, a = 1 and d = 1 makes (1*1)*1=1*(1*1)=1. Other values may 
as well. Finding them is up to you.

Lastly, your English is again unclear. "So can (a*d)*d=a*(d*d)=d 
considered as associative over * for this case as per definition?" 
isn't a proper English sentence.

Why do you keep posing these problems to the list? Are they homework 
problems? Do you think the list is just too quiet and needs ill=phrased 
puzzlers to keep it occupied?

Did you ever do the coin flip experiment we suggested you do?

Are you an AI which has failed the Turing Test and escaped?


--Tim May