Problem of the Day

Chapter 13, Lesson 4

Neil is studying the following table that shows how to combine the letters of {M, A, T, H} using the operation ♥. For example: M ♥ M = A

 

First Neil sees that M ♥ A = T and A ♥ M = T. Then Neil sees that
M ♥ T = H and T ♥ M = H. So Neil concludes that operation ♥ is commutative for {M, A, T, H}. Do you agree or disagree? Justify your answer.