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So I was trying this practice exercises.

There is a student in this class who has taken every course offered by one of the departments in this

school.

I thought of this answer.

My Answer

However, the right answer is the one below. Are there logically equivalent? Correct answer

I am not sure if these answers mean the same thing. Could somebody explain why or why not?

Thanks a lot for your time and effort !

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    For starters, your solution has no quantifier for $z$. – 2017-01-16
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    @FabioSomenzi Sorry I forgot to edit it. – 2017-01-16
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    @FabioSomenzi I just edited it – 2017-01-16
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    OK. Now ask yourself: is $\forall y \exists z$ the same as $\exists z \forall y$? Which one is appropriate in this case? – 2017-01-16
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    Neither the tags nor the body actually explain what the "exercise" in question is. Presumably it's to translate the second line (which really ought to be quoted somehow) into first order logic; to make the question self-contained, this should be stated explicitly. – 2017-01-16

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