I am reading an intro logic book and I don't know how they got the answer to one of the questions. It says to transcribe the following sentence into predicate logic,
Anyone who loves nothing without a tail owns nothing which is loved by an animal.
The transcription guide is:
$Ax$: $x$ is an animal
$Px$: $x$ is a person $\space \space \space \space $(This is used to transcribe 'anyone' as '$(\forall x)Px$')
$Lxy$: $x$ loves $y$
$Oxy$: $x$ owns $y$
$Txy$: $x$ is a tail of $y$
For my answer I got,
$( \forall x) \{ [Px \land (\forall y)(Lxy \rightarrow ( \exists z)Tzy)] \rightarrow ( \forall z)[( \exists w)(Aw \land Lwz) \rightarrow \lnot Oxz] \} $,
however the book got,
$( \forall x) \{ [Px \land (\forall y)(Lxy \rightarrow \lnot ( \exists z)Tzy)] \rightarrow ( \forall z)[( \forall w)(Aw \land Lwz) \rightarrow \lnot Oxz] \} $.
The first difference is where the first existential quantifier is and the second difference is where my second existential quantifier is.
Could someone please tell me which answer is correct?