=+10. (113) Let M= (Q, X, T) be a T-generalized state machine. Let --

be a congruence relation defined in Exercise 6. Let [x] = {y E X+

x - y} Vx E X+ and S(M) = {[x] I x E X+}. Prove that S(M)

is a semigroup, where the binary operation on S(M) is defined by

[x] [y] = [xy] V[x], [y] E S(M) .