Attachment 22004

I attached a picture of the proof. Any help is appreciated!

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- Aug 8th 2011, 03:48 PMCrayolaIS this proof valid or invalid?
Attachment 22004

I attached a picture of the proof. Any help is appreciated! - Aug 8th 2011, 04:46 PMPlatoRe: IS this proof valid or invalid?
- Aug 8th 2011, 05:04 PMCrayolaRe: IS this proof valid or invalid?
- Aug 9th 2011, 11:57 AMCrayolaRe: IS this proof valid or invalid?
- Aug 9th 2011, 12:26 PMPlatoRe: IS this proof valid or invalid?
On the set of all real numbers, let $\displaystyle P(x)$ mean “x is positive”.

$\displaystyle \neg \left( {\forall x} \right)\left[ {P(x)} \right]$ means “Some real number is not positive”. Literally, “It is false that all real numbers are positive”.

Whereas, $\displaystyle \left( {\forall x} \right)\left[ {\neg P(x)} \right]$ means “No real number is positive”. Literally, “All real numbers are not positive”.

Now can you answer the question? - Aug 9th 2011, 01:48 PMCrayolaRe: IS this proof valid or invalid?
Okay, thank you!