Propositional logic: is the logic behind my answer correct?

Question

Q: Given the following, can you prove that the unicorn is mythical? How about magical? Horned?

"If the unicorn is mythical, then it is immortal, but if it is not mythical, then it is a mortal mammal. If the unicorn is either immortal or a mammal, then it is horned. The unicorn is magical if it is horned."

A: Because each of these statements are implications, we cannot determine whether the unicorn is mythical. There is no definitive statement that leads to the conclusion that the unicorn is mythical, or not mythical.

Despite this, we can determine that regardless of whether the unicorn is immortal or mortal, it is horned. Because of this, it is also magical. So we can prove the unicorn is horned and magical, but not mythical.

Answer 1

Assuming : immortal=non-mortal.

1) $mythical(U) \to \lnot mortal(U)$

2) $\lnot mythical(U) \to (mortal(U) \land mammal(U))$

3) $(mortal(U) \to mammal(U)) \to horned(U)$

4) $horned (U) \to magical(U)$.

From 1) by contraposition :

$mortal(U) \to \lnot mythical(U)$;

with 2) and 3) :

$mortal(U) \to horned(U)$

and then, with 4) :

$mortal(U) \to magical(U)$.

So we can prove that the unicorn - if mortal - is not mythical, horned and magical.