### 1.

In the group $$\mathbb Z_8$$ compute, (a) $$6+7\text{,}$$ and (b) $$2^{-1}\text{.}$$

### 2.

In the group $$U(16)$$ compute, (a) $$5\cdot 7\text{,}$$ and (b) $$3^{-1}\text{.}$$

### 3.

State the definition of a group.

### 4.

Explain a single method that will decide if a subset of a group is itself a subgroup.

### 5.

Explain the origin of the term “abelian” for a commutative group.

### 6.

Give an example of a group you have seen in your previous mathematical experience, but that is not an example in this chapter.