Let $L(x,y)$ be the statement "x loves y", where the domain for both x and y consists of all people in the world.
Express the below statement using quantifiers and predicates.
"There is exactly one person whom everybody loves".
This can be thought of as, There exist a person X, such that all people love him and for all people Z, if everyone love Z, then this Z has to be X.
$\exists x \Biggl(\forall y \biggl(L(y,x) \land \forall z(L(y,z) \rightarrow (z=x)) \biggr) \Biggr)$
Am I in correct direction?