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Thread: binary operation

  1. #1
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    binary operation

    The given set is R-{-1}

    * is defined as a*b = a/[b+1]

    The question is whether * is a binary operation.

    My gut feeling was * should be a binary operation.

    So I tried to prove by contradiction.

    a is not equal to -1.

    b is not equal to -1.

    I assumed a*b = a/[b+1] = -1

    a + b + 1 = 0

    I got stuck.

    What to do?

    whether it is a binary operation or not?

    Is there any other way to proceed?

    kindly guide me.

    with warm regards,

    Aranga
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  2. #2
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    Re: binary operation

    Quote Originally Posted by arangu1508 View Post
    The given set is R-{-1}

    $\circ$ is defined as a$\circ b = \dfrac{a}{b+1}$
    The question is whether * is a binary operation.
    My gut feeling was * should be a binary operation.
    So I tried to prove by contradiction.
    What is $\large {1\circ-2=~?}$

    So does $\bf{\circ}$ mapp $R\setminus\{-1\}\times R\setminus\{-1\}\to R\setminus\{-1\}~?$ ans: No. why?

    Now the answer really depends upon how binary operation is defined in your course
    Thanks from arangu1508 and topsquark
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  3. #3
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    Re: binary operation

    It is given as * on R-{-1}.

    Thank you. I think it is not a binary operation.

    with warm regards,

    Aranga
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  4. #4
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    Re: binary operation

    You said
    The given set is R-{-1}

    * is defined as a*b = a/[b+1]

    The question is whether * is a binary operation
    My first reaction would be that a and b are two objects so, yes, this is a binary operation. If the question had been "is this a binary operation on R- {-1}", so that every (a, b) with both a and b in R- {-1} is mapped to a member of R-{-1}, then I would say no because of Plato's example.
    Thanks from topsquark
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  5. #5
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    Re: binary operation

    Thanks. I understood the difference.

    The question is what is defined as * on R-{-1} is to be tested whether it is a binary operation or otherwise.

    with warm regards

    Aranga
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