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Sets and groups

  1. Feb 20, 2009 #1
    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. jcsd
  3. Feb 20, 2009 #2

    lanedance

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    Homework Helper

    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
  4. Feb 20, 2009 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

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