For every person x , if person x is a student in this class then x has studied Calculus
This must be true for every person , here the UoD is all the people in this universe.
Now if a person is a person belonging to the class , he must know Calculus , what if the person doesn't belong to the class and knows Calculus?
Here , "if person x is a student in this class then x has studied Calculus" is an implication statement , so even if some person doesn't belong to the class , he might or might not know calculus .
What should the answer be then?
$\forall x(S(x) -> C(x))$.
What's the interpretation of this statement?
Let's take $x = \{"Ram","Shyam","Seeta","Geeta"\}$.
Ram and Shyam belong to the class and know Calculus , and Seeta and Geeta do not belong to the class but they also know Calculus.
Then,
$(S(Ram))->C(x)) \ and (S(Shyam)->C(Shyam)) \ and \ (S(Seeta)->C(Seeta)) \ and (S(Geeta)->C(Geeta))$
The above entire formula must be true , It will be false only in one case , if Somebody is a member of the class and doesn't know Calculus.
Why the other one is wrong?
$\forall x(S(x) and C(x))$. It would be true if and only if both S(x) and C(x) is true for every $x \in UoD$ .
This does not handle the case if $x$ doesn't belong to the class and knows Calculus.