# DM-Groups and Lattice-Q7

+1 vote

For a positive number c, consider the open interval $G = (-c, c)$ of real numbers. For $x, y \in G$, define

$x*y:=\frac{x+y}{1+xy/c^2}$

Which one of the following statements is true?

(A).G is monoid but not group

(B).G is a group but not abelian

(C).G is semigroup but not a monoid

(D).G is an abelian group