# Sets and groups

1. Feb 20, 2009

### duki

1. The problem statement, all variables and given/known data

Let S be the set of all real numbers except -1.
Define * on S by:

a * b = a + b + ab

2. Relevant equations

i) find 3 * 5
ii) find -2 * 6
iii) show that S with the operation * is a group
iv) find a solution of the quation 2 * x * 3 = 7 in S

3. The attempt at a solution

Ok, I have no clue on these. Here is what I've attempted:

i) 28
ii) -8
iii) ???
iv) ???

Could someone give me a hand? :)

2. Feb 20, 2009

### lanedance

Need to show the set & * satisfy the group axioms
see http://en.wikipedia.org/wiki/Group_(mathematics)" [Broken]

they are:
1. closure
2. associativity
3. identity
4. inverse element

so for exmpale to show closure, this means for evry 2 elemnt a,b in G, a*b is also in G, so try to show no 2 elements a,b in G can have a*b = -1, as this is the only number not in G

associativity try writing it out & rearranging, then try and find equations for the last 2 given an element

for question iv) try writing it out

Last edited by a moderator: May 4, 2017
3. Feb 20, 2009

### HallsofIvy

Staff Emeritus
First (i) is not 28. Since that is just simple arithmetic and you got (b) right, I assume that is a typo.