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Math Help - Proofs!

  1. #1
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    Proofs!

    Using any multiplication and addition axioms that you know, prove this theorem.

    If each of x and y is a number, then
    Part one: (-x)*y = -(x*y) = x*(-y) and
    Part two: (-x)*(-y) = x*y.

    Part three: Also, if x is a number, then (-1)*x = -x. (-1)*(-1) = 1.


    I think it would obviously be easier to do each part separately but I don't know where to start. I'm sure it would be useful to use the definition of minus x in there somewhere, too.
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  2. #2
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    Quote Originally Posted by noles2188 View Post
    Using any multiplication and addition axioms that you know, prove this theorem.

    If each of x and y is a number, then
    Part one: (-x)*y = -(x*y) = x*(-y) and
    Part two: (-x)*(-y) = x*y.

    Part three: Also, if x is a number, then (-1)*x = -x. (-1)*(-1) = 1.


    I think it would obviously be easier to do each part separately but I don't know where to start. I'm sure it would be useful to use the definition of minus x in there somewhere, too.
    (-x)y + xy = (-x+x)y = 0y = 0 \implies (-x)y = -(xy)
    x(-y) + xy = x(-y+y) = x0 = 0 \implies x(-y) = -(xy)

    The others follow from these two.
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