Let S(x) :- x is a student and Exam(x,y) :- x gave exam in stream y.
The statement is ' There does not exist a student who has given exam in every stream '
I thought to negate this sentence so that i can convert it easily.
1) Not ( There exists a student who has given exam in every stream).
2) Not ( There exists a student who has not given exam in at least one stream).
I am not sure which of the above 2 is correct. While negating should I negate only the 'exists' part or whole thing including 'exists' like in 2nd sentence?
The Statement can be expressed as: $$\neg (\exists x( S(x) \wedge \forall y E(x,y)))$$ using the first interpretation which is the correct negation of the intended statement.