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Math Help - I need help with these 7 discrete math proofs

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    1

    I need help with these 7 discrete math proofs

    2.
    Let D = R. Let P(x) denote the propositional function “2x  x”. Is 8x P(x) true
    or false? Prove your answer is correct. If we change
    D to Z+, does this change the truth
    value of
    8x P(x)? Why or why not?

    3.
    Let P(x) denote the propositional function “x2 + 1 = 0”. Can we determine whether
    or not
    9x P(x) is true or false without further information? Justify your answer.

    4.
    Let D = R, and let P(x, y) denote the propositional function “x + y = 1”.
    (a) Is
    8x9y P(x, y) true or false? Justify your answer.
    (b) Is
    9y8x P(x, y) true or false? Justify your answer.

    5.
    Let D denote the set of all children in the world. Let P(x, y) denote the propositional
    function “
    x plays with y.” Translate the following quoted statement into discrete math
    notation, using quantifier symbols and
    P(x, y): “Every child plays with some child.”

    6.
    (a) Let
    D = R. Is the quantified statement 8x9y (x > y) true or false? Prove your
    answer is correct.
    (b) Let
    D be the set of strictly negative integers. Is the quantified statement

    8
    x9y (x < y)
    true or false? Prove your answer is correct.

    7.
    Let P(x, y, z) be a propositional function. Use the Generalized DeMorgan’s Laws for
    Logic to negate the following:
    (a)
    8x9y8z P(x, y, z)

    (b)
    9x8y9z P(x, y, z)
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  2. #2
    Flow Master
    mr fantastic's Avatar
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    Please don't post more than two questions in a thread. Otherwise the thread can get convoluted and difficult to follow. Start new threads as necessary for remaining questions. eg. If you have five questions, post two of them in two threads and start a new thread for the remaining one etc.

    Thread closed.

    And if the question has more than two parts to it, it is best to post only that question and its parts in the thread and start a new thread for other questions.
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