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Associative Law help pleasethanks!

  1. Feb 12, 2008 #1
    Associative Law....help please..thanks!

    b1. The problem statement, all variables and given/known data[/b]

    On the set of real numbers R, the following is defined *:RxR arrow R
    (x,y) arrow x*y=a(x+y)-xy
    find all the values of the real parameter a such that the operation is associative

    2. Relevant equations

    associative law states x*(y*z)=(x*y)*z

    3. The attempt at a solution

    x*y = a (x+y) - xy = ax + ay - xy
    (m*n) * o = m * (n*o)

    (am + an - mn) * o = m * (an + ao - no)
    a(am + an - mn) + ao - o (am + an - mn) = am + a (an + ao - no) - m (an + ao - no)
    aam + aan - amn + ao - amo - ano + mno = am + aan + aao - ano - amn - amo + mno
    am + o = m + ao
    am - ao = m - o
    a (m - o) = m - o

    a = 1 if m does not equal o, and a does not equal 0 if m = 0

    im unsure of my solution...any help would be awesome!
  2. jcsd
  3. Feb 13, 2008 #2


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    Why switch to m, n, and o? x, y, and z were working fine!

    (Oh, and never use "o" as a symbol for a number- it looks too much like 0 and is too confusing.)

    Looks to me like you have it! Remember this a must work for all m! If a must be 1 whenever m does not equal to 0 (and certainly there will are numbers that are not equal to 0!) you had better take a= 1.

    As far as "a does not equal 0 if m= 0", I see no problem. 1 is not equal to 0!
  4. Feb 13, 2008 #3
    would it be wrong to use m, n and p?
    also the way i have presented the answer is it legitimate?
  5. Feb 13, 2008 #4


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    No, it's just that after you have written it in terms of x, y, z, I see no reason to change to other symbols.

    Yes, just note that in order that your equations be true for all x, y, z, a must be equal to 1.
  6. Feb 28, 2008 #5
    Thanks so much for your help!
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