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Math Help - Operations - help!

  1. #1
    Junior Member
    Joined
    Nov 2008
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    45

    Operations - help!

    Hi,

    There is one part to this question I'm not sure about, part c:

    consider the following relations on the set of positive integer numbers, N.
    1.m*n= 2m-n
    2.m*n= 3mn +5
    3.m*n= 2 + cos (m+n/2 π ) (m+n/2) pi
    4.m*n= √mn root (m x n)
    5.m*n= (mn(n+1))/2

    a. Which define an operation? My answer is 2, 3 and 5
    b. Which of the above equations define a commutative operation? My answer is 2 and 3. 5 is not and the other two are n/a as they are not operations.
    c. Do any of the above operations admit an identity? This is the question I'm not 100% sure about. I can't see any so am tempted to say no but could anyone else offer any advise if I am missing something?

    Thanks
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  2. #2
    Member
    Joined
    Aug 2008
    Posts
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    Do you mean m*n=2-cos((m+ \frac{n}{2})\pi)? If so then work our 1*2 and 2*1. What do you get? What does this mean?

    As for identities, I believe there aren't any. However 5 has a right identity.
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