three kinds of "only"

The person that no one likes(not really), the only self-admirer and the narcissist---

(i) Only Bill likes Bill.
v: for all
b: Bill
Lxy: x likes y

Vx(Lxb -> x=b )


(ii) Only Bill likes himself.

Vx(Lxx -> x=b)


(iii) Bill likes only himself.

Vx(Lbx -> x=b)