= Solution
The supervisor can depend on the student, so the <existential quantification> belongs inside the <universal quantification>:
$$
\boxed{\forall x\bigl((\mathit{Undergrad}(x)\lor\mathit{Masters}(x))\to\exists y\,\mathit{SupervisedBy}(x,y)\bigr).}
$$
The <first-order sentence> permits different students to share a supervisor. It requires neither that the supervisor be different from the student nor that the supervisor be a faculty member, since neither additional condition was given.
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