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Thread: An inequality

  1. #1
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    An inequality

    Please consider the following. Either prove or give a counter-example.
    If $\large 0\le a\le x\le 1~\&~0\le b\le y\le 1$ then $\large a+b-a\cdot b\le x+y-x\cdot y$
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  2. #2
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    Re: An inequality

    Quote Originally Posted by Plato View Post
    Please consider the following. Either prove or give a counter-example.
    If $\large 0\le a\le x\le 1~\&~0\le b\le y\le 1$ then $\large a+b-a\cdot b\le x+y-x\cdot y$
    This is related to "probability of union" post, yes?

    It appears true, I haven't been able to find a counter example but also haven't been able to prove it (yet).
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  3. #3
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    Re: An inequality

    $\displaystyle 1-a\geq 1-x \geq 0$

    $\displaystyle 1-b\geq 1-y\geq 0$

    Multiply

    $\displaystyle (1-a)(1-b)\geq (1-x)(1-y)$
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