# Introduction to Abstract Algebra/Problem set 3

## Derivations of PropertiesEdit

In the following exercises, you are prompted to give proofs which support the statements. Let denote the identity element of some group.

- Prove that if or , then .
- Prove that if , then .

In the following exercises, you are prompted for proofs supporting the statements regarding various subsets of the real numbers, . For reference, and .

- Prove that is a group where for .
- Prove that does not form a group.
- Prove that a homomorphism from to exists.
- Prove that a homomorphism from to exists.
- Prove that there is a bijection, for which it is true that and . We say that is an isomorphism between the two groups.