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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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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(Solved): Let \( x \) and \( y \) be real numbers such that \( x-y \) is irrational. Define sets \( U \) and ...

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