Prove if x+y is irrational then x or y are irrational.

For real numbers x and y prove if x+y is irrational then x or y are irrational.

This is a proof by contraposition, so we assume x and y are rational.

then x=m/k and y=n/t where m,k,n,t are integers.

so x+y = m/k + n/t = (mt + nk)/(kt) which is rational since m t n k are integers.

So x+y is rational. Therefore, by contraposition (~q=>~p therefore p=>q), if x+y is irrational then x or y are irrational.