Homework Assignment 5 - Due Wednesday, November 4

profedgar 26 Oct 2009 21:41

Section 8: 1, 2, 5, 6, 9, 11, 12, 16, 30, 33, 35cefgh, 40, 46, 48.

**Extra Problem:**

Let $G$ be a group, and let $H$ be a subgroup. We define a relation $\sim_H$ on the group in the following way. For any two elements $a,b\in G$, we let $a\sim_H b$ if and only if $ab^{-1}\in H$. Prove that $\sim_H$ is an equivalence relation.