Binary Operations : Cayley Table
Consider the Cayley table: (see file)
Show that there is only one way to complete table (1) so that the resulting operation is associative, and that the result makes {a,b} into a commutative monoid.
© BrainMass Inc. brainmass.com March 4, 2021, 5:49 pm ad1c9bdddfhttps://brainmass.com/math/discrete-math/binary-operations-cayley-table-12810
Solution Preview
Proof. Denote the binary operation by *. By the hypothesis, we know that a*b=b and b*b=a. ...
Solution Summary
A Cayley table is completed so as to satisfy set conditions. The associative operation resulting from a commutative monoid is determined.
$2.19