4 votes 4 votes Let $\text{G}$ be a group. Let $g,h,x,y \in \text{G}$ be given. It is given that $x \ast g = h, y \ast g = h$ $x = y$ $x \ast x \ast x = y \ast y \ast y$ $x \ast y \ast x = y \ast x \ast y$ Only I Only II Only I and III All of I, II and III Set Theory & Algebra goclasses2024-dm-3-weekly-quiz goclasses set-theory&algebra group-theory 2-marks + – GO Classes asked Apr 27, 2022 • retagged May 4, 2023 by Lakshman Bhaiya GO Classes 274 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
3 votes 3 votes Since, $x\ast g = y\ast g,$ So, by the right cancellation property of a group, we have $x= y.$ So, All three statements are correct. GO Classes answered Apr 27, 2022 GO Classes comment Share Follow See all 0 reply Please log in or register to add a comment.
