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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- Aug 2nd 2011, 11:33 AMdemarkusSheffer 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? - Aug 2nd 2011, 12:07 PMPlatoRe: Sheffer stoke help please
This is a real mess.

We use

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

$\displaystyle \begin{align*}P \wedge (\neg Q \vee R) &\equiv P \wedge \left( {(Q|Q) \vee R} \right) \\ &\equiv \left\{ {P|\left[ {\left( {(Q|Q)|(Q|Q)} \right)|\left( {R|R} \right)} \right]} \right\}|\left\{ {P|\left[ {\left( {(Q|Q)|(Q|Q)} \right)|\left( {R|R} \right)} \right]} \right\} \end{align*}$

I hope this helps.