DM-Groups and Lattice-Q6

+1 vote

Let g,h,x,y \in G be given. It is given that x*g=h, y*g=h.

\text{I. }x=y

\text{II. }x*x*x = y*y*y

\text{III. }{x*y*x = y*x*y }

(A).Only \text{I }

(B).Only \text{I }\text{I }

(C).Only \text{I } and \text{I }\text{I }\text{I }

(D).All of \text{I }\text{I }\text{I } and \text{I }\text{I }\text{I }

asked Jul 8 in Discrete Maths by gbeditor (23,750 points)
reshown Jul 9 by gbeditor

2 Answers

–1 vote
All are correct d)
answered Jul 9 by tsnikhilsharmagate2018 (31,010 points)
how to get the first part, second and third can be derived from first
does G here means group?
0 votes
Given :

x*g = h -----1

y*g= h ------2

Equate 1 and 2

x*g = y*g

Now using cancellation property, g is cancelled on both sides.

==> x = y

Now II and III can be easily proved using this.
answered Sep 22 by ts1505240048 (1,930 points)