"Everyone is loved by someone or other"
I'm not sure how to translate this into predicate logic. At first, I said $\forall x\exists y,Lyx$ where $Lxy$ is x loves y. However, it is not true that there is someone who loves everyone. The sentence says that "everyone" is loved by someone or other (i.e. everyone in the domain is loved). Would it be correct to say $\exists x \exists y Lxy$ , but I don't think that 'x' in this case covers everyone in the domain.