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Math Help - To show the function in disjunctive normal form

  1. #1
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    To show the function in disjunctive normal form

    Hi guys!
    Problems with discrete mathematics, really need your help.
    I did the truth table:


    But can not understand how to make the following points:
    to show the function in disjunctive normal form; - Done
    to show the function as a polynomial Zhegalkin; - Done
    Minimize the basis of DNF; - Done
    show the minimum function in the bases Schaeffer and Pierce

    Please Help!
    Last edited by dotexe; January 15th 2012 at 01:04 PM.
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  2. #2
    MHF Contributor
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    Re: To show the function in disjunctive normal form

    There is nothing difficult in writing functions in the bases of Sheffer and Pierce, but the results are probably going to be too long. For Sheffer stroke | (NAND) we have \neg P=P\mid P, P\land Q=(P\mid Q)\mid(P\mid Q) and P\lor Q=(P\mid P)\mid(Q\mid Q). For Peirce arrow \downarrow (NOR) we have \neg P=P\downarrow P, P\land Q=(P\downarrow P)\downarrow(Q\downarrow Q) and P\lor Q=(P\downarrow Q)\downarrow(P\downarrow Q). You see that formulas occur two times in the translation. I would write a program in some language that can handle inductive datatypes (such as ML or Scheme) to convert formulas to Sheffer and Pierce bases.
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