Re: Q on associative binary operation

On Thu, Aug 28, 2003 at 12:14:20AM -0700, 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?

a d d d \ / \ / d d a d \ / \ / d = d What's the problem?