implication versus conjunction correctness in FOL? I've just started learning FOL and I'm really confused about whether to use conjunction or implications. For example, if I want to represent
some students who answer the easiest question do not answer the most difficult

I came up with several solutions that seem equivalent to me.
1) ∃x. (student(x) Λ solve(x, easy) Λ ¬solve(x, hard))
2) ∃x. (student(x) -> (solve(x, easy) Λ ¬solve(x, hard)))
3) ∃x. ((student(x) Λ solve(x, easy)) -> ¬solve(x, hard)))
Can anyone explain which is correct and why the others are wrong?

One way to look at it is to translate the logical statements into more everyday language, and see what they actually say.
1) There exists someone who is a student, answered the easy question, and didn't answer the hard question.
2) There exist someone who, if they are a student, answered the easy question and not the hard one (but if they're not a student we know nothing about what questions they answered).
3) There exists someone who, if they are both a student and answered the easy question, did not answer the hard question (if they are not a student, we do not know which questions they answered; if they are a student but did not answer the easy question we do not know if they answered the hard one).
