Take A (“First-year students… like to enter for the prize”), E (“All University students are eligible to enter for the prize”), and F (“All those who like to are entitled to enter for the prize”):
- From A and F: If first-year students like to enter, and all who like to enter are entitled, then first-year students are entitled to enter.
- E is consistent with this — if University students are eligible, first-year students (as part of University students) can be eligible.
- Together, these three connect liking, entitlement, and eligibility without contradiction.
Other sets break the link or introduce unrelated conditions (e.g., rankings or partial subsets) without forming a neat chain.