Consider the following usages:
Either the book and the pen are neither in the pocket nor in the backpack of either Sally or Peter.
Both the book and the pen are neither in the pocket nor in the backpack of either Sally or Peter.
Both the book and the pen are not in the pocket or the backpack of Sally and Peter.
Which of the three sentences is correct?
What I am trying to mean is that "the book is not in the pocket of Sally; the book is not in the backpack of Sally; the book is not in the pocket of Peter; the book is not in the backpack of peter". And same thing for the book.
Can they be improved?
The question focuses on the word usage and English grammar of "either", "neither", and "both". This is strictly not a logic puzzle because meaning is very clear: nothing is the pocket of anyone.