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Hello,

So someone just asked me for assistance on a proof, and while I'm fairly certain you can't do what he did, I am not completely sure on the reasons.

To state it as formal logic,

If you have proposition A:

[tex]P \rightarrow Q[/tex]

And let's call proposition B

[tex]\neg (P \rightarrow Q)[/tex]

If you were to show B was false, then I think that does not imply A is true.

Am I right? And what logic is really going on above?

Thanks for any help you can provide.

EDIT:

I tried looking at the implication as,

[tex] P \rightarrow Q \equiv \neg P \vee Q[/tex]

which means that

[tex]\neg (P \rightarrow Q) \equiv P \wedge \neg Q[/tex]

which no longer seems to be really an implication statement.

So someone just asked me for assistance on a proof, and while I'm fairly certain you can't do what he did, I am not completely sure on the reasons.

To state it as formal logic,

If you have proposition A:

[tex]P \rightarrow Q[/tex]

And let's call proposition B

[tex]\neg (P \rightarrow Q)[/tex]

If you were to show B was false, then I think that does not imply A is true.

Am I right? And what logic is really going on above?

Thanks for any help you can provide.

EDIT:

I tried looking at the implication as,

[tex] P \rightarrow Q \equiv \neg P \vee Q[/tex]

which means that

[tex]\neg (P \rightarrow Q) \equiv P \wedge \neg Q[/tex]

which no longer seems to be really an implication statement.

Last edited: