-(p↓q)⇐⇒(-p↑-q)

I need to prove this but are not sure what the down and up arrows mean.

Do I have to construct a truth table?

Thanks,

Chris

(Doh)

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- Nov 26th 2012, 07:14 AMwattskickinNeed help with a proof
*-(p*↓*q)*⇐⇒*(-**p*↑-*q)*

I need to prove this but are not sure what the down and up arrows mean.

Do I have to construct a truth table?

Thanks,

Chris

(Doh) - Nov 26th 2012, 08:11 AMPlatoRe: Need help with a proof
So far as I know the definitions vary here. I can give you the one used by WVO Quine:

$\displaystyle \begin{array}{*{20}c} P &\vline & Q &\vline & {P \uparrow Q} \\\hline {T} &\vline & {T} &\vline & {F} \\ {T} &\vline & {F} &\vline & {T} \\ {F} &\vline & {T} &\vline & {T} \\ {F} &\vline & {F} &\vline & {T} \\ \end{array} $ and $\displaystyle \begin{array}{*{20}c} P &\vline & Q &\vline & {P \downarrow Q} \\\hline {T} &\vline & {T} &\vline & {F} \\ {T} &\vline & {F} &\vline & {F} \\ {F} &\vline & {T} &\vline & {F} \\ {F} &\vline & {F} &\vline & {T} \\ \end{array} $ - Nov 26th 2012, 08:28 AMemakarovRe: Need help with a proof
I agree. The notations $\displaystyle \downarrow$ and $\displaystyle \uparrow$ probably refer to Peirce's arrow (NOR) and Sheffer stroke (NAND), respectively.

This depends on the assignment. There are many ways of proving a propositional formula, from constructing a truth table to giving a derivation in one of many formal systems. - Nov 26th 2012, 09:11 AMwattskickinRe: Need help with a proof
Attachment 25942I constructed the following truth table and looking at the final line it appears the statement is true

- Nov 26th 2012, 09:48 AMPlatoRe: Need help with a proof
- Nov 26th 2012, 12:44 PMemakarovRe: Need help with a proof
- Nov 26th 2012, 06:22 PMwattskickinRe: Need help with a proof
Sorry, I also had to prove the formula ¬(p ↑ q)⇐⇒(¬p ↓¬q) so I added that information to the columns. since the columns for ¬(p ↓ q) equal the columns for (¬p ↑¬q) that formula is true. Since the columns for ¬(p ↑ q) equal the columns for (¬p ↓¬q) that formula is true.

Thank you for challanging me to finish thinking this problem through. I have suffered a recent brain injury and my thought process suffers from this.(Thinking)