## Formal Logic question

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tequilawine

Posts: 14
Joined: Sun Mar 22, 2015 6:11 pm

### Formal Logic question

IF you are not T, then you are not V.

Diagram: NOT T---> NOT V

The book also said V---> T.

I don't know how can it get V--->T. You are V doesn't mean you are T. am I wrong?

Thank you

The Abyss

Posts: 3367
Joined: Sun Jan 12, 2014 3:04 pm

### Re: Formal Logic question

V -> T is the contrapositive of /T -> /V. Flip and negate. They are logically equivalent.

lollsat

Posts: 56
Joined: Wed Mar 18, 2015 1:37 pm

### Re: Formal Logic question

Hey buddy! It is V---> T because that's the contrapositive to NOT T---> NOT V. If you don't know what "contrapositive" is don't worry! I was there a few months ago when I was beginning my prep. There's an article on TLS that really helped me out that explains conditional logic fundamentals. Here it is: http://www.top-law-schools.com/conditional-reasoning.html Someone will post here giving you a great explanation, still, I HIGHLY recommend going through that article as it thoroughly explains the basics. Good luck!

js1663

Posts: 216
Joined: Tue May 27, 2014 2:13 pm

### Re: Formal Logic question

OK so we had -T ----> -V right?

That means if we don't have T, we most certainly don't have V - basically we need T to have V - so if we have V, then we must have T

It follows the method used to gain a contrapositive -
If you have -T ----> - V

Switch places so it becomes -V ---->-T and then reverse signs (negative becomes positive, positive becomes negative and vice versa -

So it becomes V ----> T

__________________

Think of it in simpler terms:

If it's not round it's not a circle

So you'd have:
- (round) ---> - (circle)

Though irrelevant to LG (doesn't need to make sense if they give you a rule) but it makes sense since circles are round, so if it's not round how could it be a circle.

If you follow the contrapositive method, you'd get

circle ---> round

The rule gave us that if it's not round it can't be a circle. If it can't be a circle unless it's round, then we know that if it is a circle, then it must be round, otherwise it'd violate the original rule. Same idea with the original example of TV

tequilawine

Posts: 14
Joined: Sun Mar 22, 2015 6:11 pm

### Re: Formal Logic question

RZ5646

Posts: 2391
Joined: Fri May 30, 2014 1:31 pm

### Re: Formal Logic question

tequilawine wrote:IF you are not T, then you are not V.

Diagram: NOT T---> NOT V

The book also said V---> T.

I don't know how can it get V--->T. You are V doesn't mean you are T. am I wrong?

Thank you

The other responses explained it but they didn't prove it, so I'll give it a shot with a reductio ad absurdum:

Say you're V. Then let's assume that you're ~T (not T). But then by your first conditional you must be ~V, and we just said that you're V. You have V and ~V at the same time, which is a contradiction. Thus the assumption that you are are ~T must be false, and its opposite must be true: you are T. Thus, if you are V, you are T, and V --> T.

In general, any conditional p --> q can be flipped into ~q --> ~p. The flipped version is called the contrapositive, and it works both ways: ( p --> q ) <--> ( ~q --> ~p ).