(1)the problem whether the statemen

(1)the problem whether the statement that p and q are relative primes is false can be suspended, because even if the statement that p and q are relative primes is false, it recognizes the fact that “both p and q are integers” since the concept of co-prime and the truth or falseness are both used for two integers. Then, if the original proposition that √2=p/q (p and q are not both integers) is true, it indicates that “p and q are not both integers”, which contradicts with the meaning “that both p and q are integers” contained in the conclusion “that the statement p and q are relative primes” is false. And this indicates the statement “that the original proposition is true if the For the time being, the proof in the textbook that √2 is not rational number can be put aside, while the Counter-thesis of the proof shall be figured out at first. It’s not clear whether √2=p/q (p and q are both integers), √2=p/q (p and q are relative primes) or both are the Counter-thesis. is false” is false. That is to say, the given Counter-thesis does not conform to the requirements of reductio ad absurdum, so reductio ad absurdum can’t be applied.Note: the textbook holds that the Counter-thesis √2=p/q (p and q are relative primes) and the "(p and q are relative primes" in it all have true values, and their true values are consistent. The author adapts to this point in the above.