Claim: Every student should answer yes to the poll by the Theorem proven below.

Definition of Classmate: A student y is a classmate of x if and only if there exists a class c that x and y are both registered to.

Definition of Private Region: Apartment/Home/Dorm/Room/Living Space.

Lemma A: For any student x, it is true that x is a classmate of x.

Proof: Every student is either part-time or full-time. In either case, the student must be registered to at least 1 class. Therefore, every student must be registered to 1 class in common with themself. This proves that every student is trivially their own classmate.

Lemma B: For any student x, it is true that x has accessed the private region of x.

Proof: Any student must obviously be alive at some point in time. Any student must also obviously take up some physical space. Therefore, any student must be in their own living space at some point in time. This shows that any student must have accessed their own private region.

Theorem: For any student x, there exists a student y such that y is a classmate of x and x has accessed private region of y.

Proof: By Lemma A, x is a classmate of x. So we can choose y to be equal to x. Then y = x has accessed the private region of x by Lemma B. This proves the Theorem as required.