Assume that * is a binary operation on S with identity elements e and that x*(y*z)=(x*z)*y for all x,y,z E S. Prove * is commutative and associative!
Follow Math Help Forum on Facebook and Google+
Originally Posted by mandy123 Assume that * is a binary operation on S with identity elements e and that x*(y*z)=(x*z)*y for all x,y,z E S. Prove * is commutative and associative! If you let $\displaystyle x=e$ then $\displaystyle e(yz) = (ez)y \implies yz = zy$. This is commutative. Now $\displaystyle x(yz) = (xz)y \implies x(zy) = (xz)y$. This is associate.
View Tag Cloud