DM-Groups and Lattice-Q7

+3 votes

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


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

asked Jul 8, 2019 in Discrete Maths by gbeditor (44,970 points)
reshown Jul 9, 2019 by gbeditor

2 Answers

0 votes
D is correct one
answered Jul 9, 2019 by (34,650 points)
what will be the identity element?
because smallest positive number is always greater than zero.
can you show how u did ? that would be very helpful
solution anyone???...
+3 votes

Let, x, y \in G
\therefore x * y = \frac {x + y}{1 + \frac {xy}{c^2}} = \frac {y + x}{1 + \frac {yx}{c^2}} = y * x

\Rightarrow x * y = y * x

Therefore, G is an Abelian Group.

Also, the identity element in G is 0; and the inverse of an element x \in G is -x.

answered Sep 15, 2019 by (210 points)