(Solved):
Let \( x \) and \( y \) be real numbers such that \( x-y \) is irrational. Define sets \( U \) and ...
Let \( x \) and \( y \) be real numbers such that \( x-y \) is irrational. Define sets \( U \) and \( V \) by \( U=\{x+r: r \in \mathbb{Q}\} \) and \( V=\{y+s: s \in \mathbb{Q}\} \). Show that \( U \cap V=\emptyset \).