answer yaaro -2

first one is pretty famous..if √2 is rational, √2=p/q
p,q r natural numbers relatively prime to each oder..
2q²=p²

or p is of the form 2k

=> q²=2k²
or q also has to be of the form 2n
which is not possible as p,q supposed to be relatively prime to each oder, so √2 is irrational..
cheers!!

i think Q2 is an axiom

i dont think there are proofs for Qs like 2 parallel lines dont intersect each other etc

they are driven by definitions and human intuition