# IS this proof valid or invalid?

• August 8th 2011, 03:48 PM
Crayola
IS this proof valid or invalid?
Attachment 22004

I attached a picture of the proof. Any help is appreciated!
• August 8th 2011, 04:46 PM
Plato
Re: IS this proof valid or invalid?
Quote:

Originally Posted by Crayola
Attachment 22004
I attached a picture of the proof. Any help is appreciated!

Maybe it just my browser, but I see absolutely no proof in that link.

In any case this is true: $\neg \left( {\forall x} \right)\left[ {P(x)} \right] \equiv \left( {\exists x} \right)\left[ {\neg P(x)} \right]$
• August 8th 2011, 05:04 PM
Crayola
Re: IS this proof valid or invalid?
• August 9th 2011, 11:57 AM
Crayola
Re: IS this proof valid or invalid?
Quote:

Originally Posted by Plato
Maybe it just my browser, but I see absolutely no proof in that link.

In any case this is true: $\neg \left( {\forall x} \right)\left[ {P(x)} \right] \equiv \left( {\exists x} \right)\left[ {\neg P(x)} \right]$

Right, sorry I meant statement. So why wouldn't the given be valid?
• August 9th 2011, 12:26 PM
Plato
Re: IS this proof valid or invalid?
Quote:

Originally Posted by Crayola
Right, sorry I meant statement. So why wouldn't the given be valid?

On the set of all real numbers, let $P(x)$ mean “x is positive”.

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

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

Now can you answer the question?
• August 9th 2011, 01:48 PM
Crayola
Re: IS this proof valid or invalid?
Okay, thank you!