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Math Help - Logic garhh!! need some help

  1. #1
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    Logic garhh!! need some help

    I'm learning logic and I have to prove algebraically that:

    the AND operator may be expressed in terms of the
    NOR operator as follows: p AND q= (p NOR p) NOR (q NOR q)

    I have no idea how to work this out because I don't understand the second part. I understand p AND p perfectly well but how do I work this out using algebra?

    I used the words as I was having problems with the copy and pasting the symbols.

    Can you show me each step involved in breaking this down and working it out please I really need some help

    **EDIT**


    I have a screenshot here from a website I was refered to the other day and it proves it but doesn't show the working out... this is what I need to learn.
    Attached Thumbnails Attached Thumbnails Logic garhh!! need some help-untitled.png  
    Last edited by uperkurk; April 19th 2012 at 11:53 AM.
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  2. #2
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    Re: Logic garhh!! need some help

    Logical NOR - Wikipedia, the free encyclopedia
    "The NOR operation is a logical operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both operands are false. In other words, it produces a value of false if and only if at least one operand is true."

    When is the right side true? When both p NOR p and q NOR q are false; that is, when both p and q are true.

    For a visual explanation, see the Venn diagrams on the Wikipedia page above.

    Edit- Using sets:
    The intersection of p and q can be expressed as the complement of the union of the complement of p and the complement of q.
    Last edited by Cheerios; April 19th 2012 at 11:59 AM.
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  3. #3
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    Re: Logic garhh!! need some help

    Thanks but you haven;t really shown any working out so it doesn't help me much
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    Re: Logic garhh!! need some help

    Quote Originally Posted by uperkurk View Post
    be expressed in terms of the
    NOR operator as follows: p AND q= (p NOR p) NOR (q NOR q).
    Note that \neg \left( {p \vee p} \right) \equiv \neg p.
    Likewise \neg \left( {q \vee q} \right) \equiv \neg q.
    Then you have \neg \left( {\neg p \vee \neg q} \right) \equiv  p \wedge q
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  5. #5
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    Re: Logic garhh!! need some help

    That you so much Plato. Can you tell me which laws you used?
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  6. #6
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    Re: Logic garhh!! need some help

    Quote Originally Posted by uperkurk View Post
    Can you tell me which laws you used?
    This is not a tutorial service. So you need to learn the basic rules in the text material.
    You should have a set of basic rules.
    For example: \neg \left( {p \vee q} \right) \equiv \neg p \wedge \neg q.
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  7. #7
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    Re: Logic garhh!! need some help

    So what you wrote their is perfectly acceptable and simplified enough for full marks?
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