1. Verify whether the system is a Boolean algebra.

Discussion in 'Homework Help' started by audreyeckman, Jan 19, 2016.

  1. audreyeckman

    Thread Starter New Member

    Jan 7, 2016
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    0
    I am really struggling with this problem, and so are my friends in the same course. Please refer to PDF for the tables.
    Any help or guidance is appreciated!


    Given a mathematical system M=({0,a,b,c},#, &) where the two operators # and

    & are defined in the following two subtables.

    1. Verify whether the system is a Boolean algebra.

    2. List the complements of elements 0, a, b, and c if the system is a Boolean algebra.



    I have started a table that my professor suggested to follow on the pdf, but I have no idea how to start it.

    Another hint was that:


    I found the following link is quite useful.

    http://www.ctp.bilkent.edu.tr/~yavuz/BOOLEEAN.html

    In table 1.(b), you can find something like very similar to "0" in table 1.(a).

    Now you can say following:

    (1) Something # Something' = 0 or a or b or c,

    (2) Something & Something' = 0 or a or b or c.

    From table 1.(a) and 1.(b), you can find pairs that satisfy your (1) and (2) always.
     
  2. WBahn

    Moderator

    Mar 31, 2012
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    The first step is to make sure you understand what is required for something to be "a Boolean algebra".

    So what, in YOUR words, is required?
     
  3. audreyeckman

    Thread Starter New Member

    Jan 7, 2016
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    0
    Following the commutative, distributive, and identity laws is required I believe.
     
  4. WBahn

    Moderator

    Mar 31, 2012
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    audreyeckman likes this.
  5. Papabravo

    Expert

    Feb 24, 2006
    10,137
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    The laws that the operators must follow are only part of the story. The properties of the elements are also important.
     
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