Translating 2 place predicates

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Hi Having some trouble translating these:

Everbody likes Ray or Lucy. is it asfollows:

"∀x∃x[love'(Ray(x)+lucy)] ?

and for nobody likes the teacher ¬∃x likes'(teacher) ??

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Your notation is a bit strange. Assuming an appropriate universe of people, I would expect something more like: $$ \forall x \, [\textsf{Likes}(x, \textsf{Ray}) \lor \textsf{Likes}(x, \textsf{Lucy})] \\ \neg \exists x \, [\textsf{Likes}(x, \textsf{Teacher})] $$