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Math Help - Quantifiers question

  1. #1
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    Quantifiers question

    It's been a little why since I've had discrete math, so could someone help me remember why:

    "There exists an 'x' such that for all 'y', x + y == 0" is FALSE,

    but

    "For all 'x', there exists a 'y' such that x + y == 0" is TRUE?

    Thanks!
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  2. #2
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    Quote Originally Posted by jtc4zH View Post
    It's been a little why since I've had discrete math, so could someone help me remember why:

    "There exists an 'x' such that for all 'y', x + y == 0" is FALSE,

    but

    "For all 'x', there exists a 'y' such that x + y == 0" is TRUE?

    Thanks!
    Read it twice over and slowly. The first statement says that there is one number, x that when added to any number y, it equals zero. You cannot possibly say that both x+4=0 and x+55=0.

    The second line says that for any number x, there exists a y that satisfies those conditions. This is a one-to-one relationship. For:
    x=5,
    y=-5;

    for x=,
    y=-.
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