“Abby does not like Cody or Dana” 
In this exercise in Stanford's Introduction to Logic course, based on the given table, the final sentence "Abby does not like Cody or Dana" is considered false.
Doesn't that sentence mean "Abby doesn't like Code or Abby doesn't like Dana"? For the whole of this sentence to be true, at least one part of the two is true; so, this sentence true, isn't it?
 A: If I say "I don't eat fish or cheese" that usually means that I do not eat fish and I do not eat cheese, not that I possibly don't eat fish but I sometimes eat some cheddar, or I never touch cheese but I partake of the occasional mackerel.
So in this case the answer is correct, if she does not like Cody or Dana she doesn't like Cody and she doesn't like Dana.
It seems more of a question about English than about mathematics.
A: 
“Abby does not like Cody or Dana”

The contrived sentence “A does not like C or D” is ambiguous, as its intended meaning depends on whether ‘not’ or ‘or’ is its main connective, that is, which word is being stressed as the sentence is being read aloud:

*

*A does not like C or D
It is not that (A likes C or D)
It is not that (A like C or A likes D)
(A dislikes C) and (A dislikes D)
Idiomatic phrasing:

*

*Abby likes neither Cody nor Dana

*Abby dislikes (both) Cody and Dana



*A does not like C or D
(A does not like C) or (A does not like D)
(A dislikes C) or (A dislikes D)
Idiomatic phrasing:

*

*Abby either dislikes Cody or dislikes Dana
A: The instructor wants us to deem each relational table as depicting a possible world. Each possible world comprises some conditions. The sentences are utterances about a possible world.
In the given table (possible world), at least one of the conditions, likes(Abby, Cody) and likes(Abby, Dana), holds; we may not know which. But the given sentence expresses a denial of this, so to say, the compound condition --which may be formulated as not-likes(Abby, Cody or Dana).
