-(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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- November 26th 2012, 08:14 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) - November 26th 2012, 09:11 AMPlatoRe: Need help with a proof
- November 26th 2012, 09:28 AMemakarovRe: Need help with a proof
I agree. The notations and 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. - November 26th 2012, 10:11 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

- November 26th 2012, 10:48 AMPlatoRe: Need help with a proof
- November 26th 2012, 01:44 PMemakarovRe: Need help with a proof
- November 26th 2012, 07:22 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)