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Math Help - Write in the simplest way possible using the laws of set algebra

  1. #1
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    Write in the simplest way possible using the laws of set algebra

    Hi, got an exercise I can't seem too solve, just started with Discrete Mathematics.
    I'm supposed to write this: (A - B) (intersection) (A U B) in the simplest possible way.

    Really appreciate any help
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  2. #2
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    Re: Write in the simplest way possible using the laws of set algebra

    Quote Originally Posted by Remi View Post
    Hi, got an exercise I can't seem too solve, just started with Discrete Mathematics.
    I'm supposed to write this: (A - B) (intersection) (A U B) in the simplest possible way.
    A\setminus B=(A\cap B^c), I used the 'setminus' notation and B^c is the complement of B

    Thus (A\cap B^c)\cap (A\cup B)=[(A\cap B^c)\cap A]\cup[(A\cap B^c)\cap B].

    You should see at once how to finish.
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    Re: Write in the simplest way possible using the laws of set algebra

    ?

    But I don't quite get what you did in the second part there:
    Which law did you use ?
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    Re: Write in the simplest way possible using the laws of set algebra

    Quote Originally Posted by Remi View Post
    ?

    But I don't quite get what you did in the second part there:
    Which law did you use ?
    C\cap(A\cup B)=(C\cap A)\cup(C\cap B) that is distribution.
    Let C=(A\cap B^c)
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    Re: Write in the simplest way possible using the laws of set algebra

    Thanks, think I got it now Was my solution correct ?
    And could it be done like this:


    Given that
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  6. #6
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    Re: Write in the simplest way possible using the laws of set algebra

    Quote Originally Posted by Remi View Post
    Thanks, think I got it now Was my solution correct ?
    And could it be done like this:


    Given that
    You missed one part.
    (A\cap B^c)\cap A=A\cap B^c
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