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?
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