I arrived at the same conclusion (invalidity) as Eliran H, but for a different reason. The premises are insufficient to show, affirmatively, that persons 18 years old and older are permitted to vote. Missing that information, the reasoning fails.
Here are my notes on my attempt to reason it through:
- If Person is Underage, then they are not permitted to Vote.
1.1 If Person is permitted to Vote, then they are not Underage. Contrapositive of #1 (looking for an affirmative statement about voting).
If Person is Faculty, then they are not Underage.
If Person is Chairperson, then they are Faculty.
Partial (valid) Conclusion: If Person is Chairperson, then they are not Underage. (#2 + #3)
- Final (failed) Conclusion: If Person is Chairperson, then they are permitted to Vote.