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(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 \

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 \( U \cap V=\emptyset \).


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