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Math Help - Expressing propositions using a defined connective.

  1. #1
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    Expressing propositions using a defined connective.

    Hello!
    I need a help with some problem of discrete mathematics.

    Can someone help me to solve this problem :

    "We define the connective( / )by:
    P/Q = not(P or Q)
    Show that all proposition composed of P and Q can be only expressed thanks to this connective ( / )"
    Last edited by mr fantastic; October 14th 2009 at 05:46 PM. Reason: Changed post title
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  2. #2
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    Quote Originally Posted by Crissman View Post
    "We define the connective( / )by:
    P/Q = not(P or Q)
    Show that all proposition composed of P and Q can be only expressed thanks to this connective ( / )"
    It is useful to have the truth table for the ‘dagger connective’ (joint denial)
    \begin{array}{ccc}<br />
   P & Q & {(P \downarrow Q)}  \\ \hline<br />
   T & T & F  \\<br />
   T & F & F  \\<br />
   F & T & F  \\<br />
   F & F & T  \\ \end{array}

    I will give you the equivalent statements. But you must prove them.
    \begin{array}{ccc}<br />
   {\neg P} &  \equiv  & {P \downarrow P}  \\<br />
   {P \wedge Q} &  \equiv  & {(P \downarrow P) \downarrow (Q \downarrow Q)}  \\<br />
   {P \vee Q} &  \equiv  & {(P \downarrow Q) \downarrow (Q \downarrow Q)}  \\<br />
   {P \to Q} &  \equiv  & {\left[ {\left( {P \downarrow P} \right) \downarrow Q} \right] \downarrow \left[ {\left( {P \downarrow P} \right) \downarrow Q} \right]}  \\ \end{array}
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  3. #3
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    Thank you very much, you help me a lotttt
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