hi,
Let ~ represents a relation.
If a~b and b~a,then
a~a (by transitivity)
is an incorrect argument.
By definition of transitivity, if a~b and b~c implies
that a~c.
I was asking on the same lines if (a*d)*d=a*(d*d)=d.
By definition associativity is defined on a,b,c
element of set S and not two elements of the set.
x*y (ie, left*top) can be followed.
Regards Sarath.
--- BillyGOTO
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?
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