How to formulate these statements I have a few logic statements and am unsure how to formulate them


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*A student is excellent if he can solve all the logic questions

*No student can solve all the logic questions

*there is a logic problem no student can solve 

*No student is excellent


I was thinking of formulating it the following way:


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*forall_yS(x,y)->E(x) (for all logic questions y if solve student x questions, then x is excellent)

*~exsit_xforall_yS(x,y) (not exist student x for all questions y student solve questions)

*exist_yforall_x~S(x,y)  (exist question y for all student x student not solve question)

*~exist_xE(x)  (not exist x such that x is excellent)


How can i be sure if i'm wrong or right ?

One way to check your translations from English to logic is to  read back to yourself strictly what you have symbolized.  For example, a strict reading of your second sentence would be 
$$\lnot \exists x\forall y(S(x, y))$$
"There does not exist a something such that for all things, it is not the case that the something solves all the things." Now, you may know what you meant to say, but the bottom line is you failed to specify the kind of thing that does not exist, and the kind of things that are solved.
Correcting for that we'll create a translation key to cover all the bases. You should always do this, so you and others will understand the translation, and reproduce, more or less, the original statement.
$E(x):\;$ "$x$ is excellent."
$S_t(x):\;$ "$x$ is a student."
$Q(x):\;$ "$x$ is a logic question."
$S_o(x, y):\;$ "$x$ solves y".
Now, we translate "No student can solve all the logic questions."
$$\lnot \exists x\Big(S_t(x) \land \forall y(Q(y) \rightarrow S_o(x, y))\Big)$$
Now, using a translation key similar to the one here, try to rewrite your translations to capture all that the sentences declare.
