Assignment:
Q1. Prove that is a is a number in G, a group, and ab = b for some b of G, then a = e, the identity element of the group.
Q2. Consider the set of polynomials with real coefficients. Define two elements of this set to be related if their derivatives are equal. Prove that this defines an equivalence relation.
Q3. Let H be a subgroup of the group G. Prove that every right coset of H is a left coset of some subgroup of G.
Provide complete and step by step solution for the question and show calculations and use formulas.