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Is $\forall r \in \mathbb{R}, r^3 \notin \mathbb{Q} \implies r \notin \mathbb{Q}$ true?

True

Contrapositive;

$r = a/b \in \mathbb{Q}$ then $r^3 = a^3/b^3 \in \mathbb{Q}$

Correct?

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  • $\begingroup$ It is bad practice to say everything with symbols. Try using words instead. $\endgroup$ – Fredrik Meyer Aug 29 '16 at 7:03
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your argument is correct! Contrapositive is the way to go.

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