Predicates and quantifiers

Question

Let $L(x,y)$ be the statement "x lives with y", where the domain for both x and y is all people.

How would I describe the below using the above statement?

Nobody lives with y becomes $¬∃xL(x,y)$ if my understanding is correct, but what if the question is nobody lives with John, how do I parse this? $¬∃xL(x,John)$?

I'm just not sure how to 'inject' quantifiers into logic.

Answer 1

It's exactly the same idea as "nobody lives with $y$," in the specific case $y=\text{John}$. It's fine.