Rules for inference with quantifiers.

Question

How to formalize the below statements with rules of inference with quantifiers? Given that: C is the set of Calculus students, P is the set of Programming students and A is the set of all students.

statements:

1. if someone is a student of Calculus, then, they must study Programming.

2. if there exists at least one student of Calculus, then, all students of Programming study Calculus

3. If all students of Programming study Calculus then nobody studies Calculus.

Answer 1

1. If someone is a student of Calculus,
   then they must study Programming.

Who are "they"?

2. If there exists at least one student of Calculus,
   then all students of Programming study Calculus.

Exist x in C implies for all x, (x in P implies x in C).

3. If all students of Programming study Calculus,
   then nobody studies Calculus.

For all x, (x in P implies x in C) implies for all x, x not in C.

If perchance the intended statement were:
If all students of Programming study Calculus,
then no student studies Calculus.

For all x, (x in P implies x in C) implies
for all x, (x in A implies x not in C).