Explore BrainMass

Explore BrainMass

    Binary Operations : Cayley Table

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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 December 24, 2021, 4:52 pm ad1c9bdddf


    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.