Logic: "the cubic root of a rational number is also a rational number" I was attempting an online logical and mathematical statements self-test from the University of Toronto and came across the following statement in question 1:

The cubic root of a rational number is also a rational number.

We are asked to select an equivalent statement from the provided list. The answer turned out to be:

If $x$ is a rational number, then $\sqrt[3]{x}$ is a rational number.

Why is that?
The given statement seems to be of the form "A is also a B". 
A statement fitting that form would be "a feline is also a mammal". But this wouldn't be equivalent to "if $x$ is a mammal, then $x$ is a feline".
I actually translated the given statement as follows, but it wasn't one of the available options:

$\forall x \in \mathbb{Q}, x = \sqrt[3]{y} \Longrightarrow x \in \mathbb{Q}$

Can someone help me identify the flaws in my reasoning, and why the given answer is the correct one?

Let's firstly put aside the completely irrelevant question herein of whether the statements are true; obviously, it's not true in general that a rational number's cube root is rational. Let's look into how we rewrite statements with algebra.
While "a feline is also a mammal" becomes "if $x$ is a feline, then $x$ is a mammal", "the cubic root of a rational number is also rational" means "if $y$ is the cube root of a rational $x$, then $y$ is a rational number". Since this time two objects are named in algebra, it's more natural to rearrange the second example as "if $x$ is a rational number and $y=\sqrt[3]{x}$, then $y$ is a rational number". And it's even more natural to only have one named variable, viz. "if $x$ is a rational number, then $\sqrt[3]{x}$ is a rational number".
