One can define at most 19,683 different binary operations on a set S having exactly 3 elements.
Added by Rickey H.
Step 1
In other words, it is a function of the form: f: S × S → S Since S has 3 elements, there are 3 × 3 = 9 possible pairs of elements in S × S. For each of these 9 pairs, there are 3 possible results in S. Show more…
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