Trying to better understand the reductio ad absurdum

[charlie_sheep]

I've just started studying college math.

I read the proof by contradiction is based on the law of excluded middle. So i tried
to make a general logic structure of this kind of demonstration to see how it could use
this law. If I'm right, of course.

Let X and Y be propositions.
1. X -> Y
2. ~Y
3. X v ~X ¹
By 1 and 3 we have:
4. Y v ~X
By 2 and 4 we have:
~X
Q.E.D.

¹ - Law of excluded middle

Is this how reductio ad absurdum is made?

I mean, generally the following statement is used:
"Suppose X is true. Then Y is true. But Y is false. So X is false."

But isn't it the same thing i just did above?

I know that, probably, I'm just talking non-sense. But even so, i think this non-sense
can help you guys to help me out with my doubts.

Anyway, thank you for the attention.

My first language is portuguese and I'm not a good english writer. So if i made any english mistakes, i apologize.

 

[Bacle2]

Hi, Charlie Sheep: ( I liked your work on two and a half mep ;) )

This is my perspective: truth-tables for connectives like & , \/ , are defined so that

they are truth-preserving. An argument is valid if, by definition, whenever the

premises are true, the conclusion cannot be false. Now, if you start with a true

premise and arrive --using truth-preserving rules --to a false statement , i.e.,

a contradiction-- then your initial premise must not have been true to start with.