Could you tell me how to write a very formal proof of the statment below with the contrapositive methode, if possible.
(I know how to do it with contradiction)

Let x be a rational number and y an irrational number, then x times y is irrational.

Sincerely,
V. Uljanov

pbuk
Gold Member
The contrapositive of this is "if xy is rational then x and y are either both rational or both irrational" and this can be proved with similar steps to the proof you already have.

Thx, but I cant see how to proceed in the same manner. If xy=m/n, then x=m/(n*y), but if y is irrational I am back to the start, and cant say anything about x.

In contradiction I assumed xy=m/n, and got y=m/(n*x)=ml/nk=m'/n' (x was rational), and this lead to the contradiction of y beeing irrational from the start.

pbuk