If $L(x, y)$: “$x$ loves $y$”, the domain consists of all people in the world.
Use quantifiers to express: "There is exactly one person whom everybody loves".
- $\exists x(\forall y L(y, x) \wedge \forall z(\forall w L(w, z) \implies z = x))$
- $\exists x \forall y( L(y,x) \wedge \forall z( L(y,z) \implies z = x ))$
So, 1 is standard answer, 2 is my answer, is my answer correct?