- #1

mikael27

- 59

- 0

## Homework Statement

For each of the following definitions for a * b and a given set, determine which of the axioms

G0, G1, G2, G3 are satisfied by a * b. In which cases do we obtain a group?

1) a - b on the set Z

2)a + b - ab on the set R | {1}

3)ab on {2^n | n in Z}

## Homework Equations

## The Attempt at a Solution

The four axioms for group are:

G0 For all a, b in G, a*b in G.

G1. Associativity. For all a, b, c in G, (a * b) * c = a * (b * c).

G2. Identity. a * e = a = e * a.

G3. Inverses. a * b = e = b * a.

How am i going to check these axioms for example 1 which says a - b on the set Z ?