Question

5. Let S = (Ro, R1, R2, R3}. Find the left and right cosets of S in D.

Answer 1

we are working with Dr. Here Ro is the identity rotation. Rp is the rotation by the I R in the rotation by the angle 2+3 / 4 Thor fore R2= Rj Rq = Rh I Rz is the rotation by the angle 34 211 Thoufore Rg= Rq Rj Rq = Rp. I Note that R is the rotation by the angle 27 and therefore R = Rp = In each of the above strings, we compose from the right. Let I be the reflection. Here To is the identity Here we note that the Rol = Ro and Thanefore the set s com be written as S= {poo Rauri The set DA is a Here Jes = { Ig Ron Jalan Ja Raha Sy his Here Jo Ro = J.

A R = RA S.R. 7 = Ra Ini are Thouefore the defe costs of s, in pa 5 and gas where I in the reflection." Again syy = f Ruggy Rosso RBRP 33} at s in Da are s and us. Thoafoore the right cosets of 5 in Dq are Thor fare the left cosets of s in Dq are all & ama Yas and also the right cosets of 8 in Da are 5 and is where AT I is the reflection. The left cosets it's in. Da огли дастс , де зір өзақ Кs • 4