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I have attempted to translate the English sentence "the very best candy is chocolate" into predicate logic as follows: $$\lnot \exists x \exists y[(C_x \land \lnot C_y)\to B_{yx} ]$$ where $x$ and $y$ are candies, $C_x:x$ contains chocolate, and $B_{xy}:x$ is better than $y$.

However, the text I am using translates it as follows: $$\exists x[C_x \land \lnot \exists y(B_{yx})].$$

So my question is, is my translation equivalent to the one in the text? I am inclined to believe that my translation is simply a less concise rephrasing of the same idea, but I would like to be sure.

Edit: I think I understand it now. It is possible that I misunderstood the sentence as saying all candies containing chocolate are better than those which do not, instead of the alternative the very best candy is one which contains chocolate.

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    I believe modifying questions to include their answers is discouraged. If you want to indicate that you think the answer is correct, you should upvote and accept it. – 2017-02-21
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    I'm sorry I actually modified it before I read your answer. – 2017-02-21

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These are not mathematically equivalent. The key to seeing this is that yours has a non-trivial dependency on the value of $C_y$. We can rephrase yours as $\forall x\forall y[(C_x\land\neg C_y\land\neg B_{yx})]$ and the other as $\exists x\forall y(C_x\land\neg B_{yx})$ which might make things formally clearer.

Looking at this from an English point of view, your statement is "It is not the case that there exists two candies such that $x$ contains chocolate $y$ does not, and $y$ is better than $x$" while the book statement is "the candy that is the best contains chocolate"

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    I just realised this and noted it in my edited post. Thank you for clarifying! I am starting to understand that formal logic is a lot more precise than colloquial written language.. – 2017-02-21