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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: $$ \forall x \, [\textsf{Likes}(x, \textsf{Ray}) \lor \textsf{Likes}(x, \textsf{Lucy})] \\ \neg \exists x \, [\textsf{Likes}(x, \textsf{Teacher})] $$

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    Ok thankyou. Haven't done this before - so in 'everbody likes ray or lucy' is (x) people who like? and in no body likes the teacher (x) is the set of people who like the teacher? – 2017-01-20
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    There aren't really any sets. If I were to literally interpret the notation I used, I would read it as: "For each person $x$, either $x$ likes Ray, or $x$ likes Lucy, or $x$ likes both Ray and Lucy." and "It is not the case that there exists some person $x$ such that $x$ likes the teacher." – 2017-01-20