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"There is $x \in \mathbb{Q}$ such that $x+y \notin \mathbb{Q}$ implies $y \notin \mathbb{Q}$."

Would it be "$y \in \mathbb{Q}$ implies there is $x \in \mathbb{Q}$ such that $x+y \in \mathbb{Q}$"?

..or an $x \notin \mathbb{Q}$?

Stackman
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1 Answers1

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Neither. It would be: If $y$ is rational there is NOT a rational number $x$ where $x + y$ is irrational.

Or you could alternatively state it as: If $y$ is rational and $x$ is rational then $x + y$ is rational.

fleablood
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  • so what would the contrapositive of "there exists an integer n such that ny is irrational => y is irrational" be? i think i've done this all wrong |:( –  Oct 24 '18 at 05:53
  • If $y$ is rational than then there does NOT exist an integer $n$ so that $ny$ is irrational. Or in other words. If $y$ is rational then for all integers $n$ we have $ny$ is rational. – fleablood Oct 24 '18 at 05:55