Question

Students of all departments who have successfully completed registration are eligible to vote. By the due date, noneof the students from the Department of Human Sciences (HS) had completed registration. Which set(s) of statements can be inferred with certainty? \[ \begin{array}{l} \text{(i) All ineligible students would certainly belong to HS.}
\text{(ii) None from non-HS departments failed to complete registration on time.}
\text{(iii) All eligible voters would certainly be students not from HS.} \end{array} \]

• A. (i) and (ii)
• B. (i) and (iii)
• C. only (i)
• D. only (iii)

Hint:

When a statement says "none of group X satisfied condition C," you can conclude "all who satisfied C are not from X," but you cannot conclude anything about how many non-X failed C unless explicitly stated.

Answer 1

The Correct Option is D

Step 1: Translate the givens.
Eligible $\Leftrightarrow$ completed registration.
Given: No HS student completed registration $\Rightarrow$ every HS student is ineligible.

Step 2: Test each statement.
(i) "All ineligible are HS." This would exclude the possibility that any non-HS student also failed to register. The prompt does not tell us whether some non-HS students missed the deadline. Hence (i) is not certain.
(ii) "No non-HS student failed." Same issue; we have no information about completion rates outside HS. Not certain.
(iii) "All eligible voters are non-HS." Since no HS student completed registration, any eligible voter must be from a department other than HS. This does follow with certainty.

Final Answer:\; \[ \boxed{\text{only (iii)}} \]