Question: 2. Understanding Groups: Part One. In this problem we shall derive some basic results based on the denition of groups as introduced in the lectures.

2. Understanding Groups: Part One. In this problem we shall derive some basic results based on the denition of groups as introduced in the lectures. Let (G, 0) be a group and let 6 be the identity element of the group. (a) (5 points) Prove that it is impossible that there exists a, b, c e G such that a 75 b but a o c = b o c. Solution

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