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.