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Math Help - Sheffer stoke help please

  1. #1
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    Sheffer stoke help please

    got stuck on the second part of this question.

    show that
    P Λ Q ≡ (P l Q)l(P l Q)
    ≡ ~((P l Q)Λ(P l Q))
    ≡~ (P l Q)
    ≡ ~(~(P l Q)
    ≡ P Λ Q

    use part 1 as example to write P Λ (~Q ∨ R) using only Sheffer stokes?
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  2. #2
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    Re: Sheffer stoke help please

    Quote Originally Posted by demarkus View Post
    got stuck on the second part of this question.
    use part 1 as example to write P Λ (~Q ∨ R) using only Sheffer stokes?
    This is a real mess.

    We use
    \begin{align*}  \neg P &=\text{ df  }P|P \\  P\wedge Q &=\text{ df  } (P|Q)|(P|Q) \\ P\vee Q &=\text{ df  }(P|P)|(Q|Q)  \end{align*}

    \begin{align*}P \wedge (\neg Q \vee R) &\equiv P \wedge \left( {(Q|Q) \vee R} \right) \\   &\equiv \left\{ {P|\left[ {\left( {(Q|Q)|(Q|Q)} \right)|\left( {R|R} \right)} \right]} \right\}|\left\{ {P|\left[ {\left( {(Q|Q)|(Q|Q)} \right)|\left( {R|R} \right)} \right]} \right\} \end{align*}
    I hope this helps.
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