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?
2026-04-02 15:13:57.1775142837
Is $\forall r \in \mathbb{R}, r^3 \notin \mathbb{Q} \implies r \notin \mathbb{Q}$ true?
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your argument is correct! Contrapositive is the way to go.