## Logical Proof

Philosophical, mathematical and computational logic, linguistics, formal argument, game theory, fallacies, paradoxes, puzzles and other related issues.

### Logical Proof

How do I prove p for p->q ?

Do I simply apply modus tollens then apply negation?

So

1) p->q
.....
2) ~q ...... Assumption
3) ~p ...... 1,2, modus tollens
4) p ..... 3, negation

Is that it?

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### Re: Logical Proof

No one? I guess I'll take it as being correct for now. I don't see how it is wrong at the moment other than I think I should have written "supposition" instead of "assumption" ... still confusing some the terminology :S

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### Re: Logical Proof

BadgerJelly » September 25th, 2017, 2:01 am wrote:How do I prove p for p->q ?

You can't. p can be False yet p->q is True. In fact that is ALWAYS the case. If p is False then p->q is True. That's material implication. From p->q you can't conclude p.

Remember, if 2 + 2 = 5 then I am the Pope. That is a true material implication. You cannot conclude that 2 + 2 = 5. From a false premise, anything follows.
someguy1
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Joined: 08 Nov 2013

### Re: Logical Proof

It's a conditional proof.

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### Re: Logical Proof

BadgerJelly » October 1st, 2017, 7:05 am wrote:It's a conditional proof.

What you wrote bears no relation to what a conditional proof is.

https://en.wikipedia.org/wiki/Conditional_proof

A conditional proof shows that q follows from p, or in other words p -> q.

You can't conclude p from that. p could be false and the material implication would still be true.
someguy1
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Posts: 539
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### Re: Logical Proof

I messed up!

Should be ...

1- p -> q
2- ~q
----
3- p ........ assumption
----
4- q
5- ~q

Therefore ~p (reductio ad absurdum), but also the same thing in this instance as Modus Tollens (denying the consequent).

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### Re: Logical Proof

BadgerJelly » October 1st, 2017, 1:06 pm wrote:I messed up!

Should be ...

1- p -> q
2- ~q
----
3- p ........ assumption
----
4- q
5- ~q

Therefore ~p (reductio ad absurdum), but also the same thing in this instance as Modus Tollens (denying the consequent).

Right. From p -> q we may infer ~q -> ~p. In this case ~q -> ~p is called the contrapositive of p -> q. It's a common proof technique in math. Same thing as modus tollens.
someguy1
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Posts: 539
Joined: 08 Nov 2013