I am trying to transcribe the following predicate logic sentence into English,
$ ( \forall x)( \forall y)[Dx \rightarrow (Cy \rightarrow Lxy)] $
I transcribed this as 'Every dog loves every cat.' However, the book I am using says the answer is 'All dogs and cats love each other.' I would've thought that the latter answer transcribes to predicate logic as,
$ ( \forall x)( \forall y)[Dx \rightarrow (Cy \rightarrow (Lxy \land Lyx))] $
Could someone please clarify this?