Proof involving Fermat's Theorem. I believe I know the answers to most of $a$.

i. the quantifier is signifies for all and in this problem it is the symbol $ \forall $. 

ii. the variables are $n, a, b$ and $c$ with $n&gt;2, c&gt; 0, b&gt;0$ and $c&gt;0$.

iii. the predicate is that $a^n + b^n\ne c^n$. (not sure about this)

However, I am lost on part b, because I do not understand how this has to do with Fermat's theorem because Fermat's theorem is focused around numbers.
An implication "$P \implies Q$" is always valid if $P$ is false. This is because an implication is somewhat like a promise: "given that the left side is true, I guarantee the right side is true". Thus if the left side is not true, all bets are off, because no one can give you a proof of the left side, and so you can promise whatever you want. "Given that pigs can fly, I can prove Fermat's Last Theorem": no one will ever be able to disprove this claim, because first they would have to demonstrate pigs flying.
the statement is correct but it doesn't prove the Fermat Last Theorem. For to prove it, it should come from well established axioms,lemmas, and theorems.. truth of the statement does not necessarily imply proof of the implication.