Contrapositive of"If $h \in \mathbb Q$ then $\exists a,b \in \mathbb Z$ such that $h=\frac{a}{b}$"

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I think the contrapositive of "If $h \in \mathbb Q$ then $\exists a,b \in \mathbb Z$ such that $h=\frac{a}{b}$" is "If $\nexists a,b \in \mathbb Z$ such that $h=\frac{a}{b}$ then $h \notin \mathbb Q$. But I'm not sure if I'm correct because I know that the statement "If $h \notin \mathbb Q$ then $\nexists a,b \in \mathbb Z$ such that $h=\frac{a}{b}$" is true which makes me think that my answer isn't correct.