Question

Students of all the departments of a college who have successfully completed the registration process are eligible to vote in the upcoming college elections. By the due date, none of the students from the Department of Human Sciences had completed the registration process. Which set(s) of statements can be inferred with certainty?
(i) All those students who would not be eligible to vote would certainly belong to the Department of Human Sciences.
(ii) None of the students from departments other than Human Sciences failed to complete the registration process within the due time.
(iii) All the eligible voters would certainly be students who are not from the Department of Human Sciences.

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

Hint:

In inference questions, separate necessary from sufficient conditions. Here, "completed registration $\Rightarrow$ eligible" does not imply the converse, and saying "none from HS completed" rules out HS from the eligible set but tells you nothing definite about completion in other departments.

Answer 1

The Correct Option is D

Given rule: Eligible voters $\Rightarrow$ completed registration.
New fact: No Human Sciences (HS) student completed registration by the due date. 

Test (iii).
If eligibility requires completion, and HS has zero completers, then no HS student can be eligible. Hence any eligible voter must come from a non-HS department. Statement (iii) is certainly true. 

Test (i).
(i) claims: "All ineligible students are certainly HS." But it is possible that some non-HS students also failed to complete registration and are therefore ineligible. The premise does not say all non-HS students completed. Thus (i) is not certain (could be false). 

Test (ii).
(ii) claims: "No non-HS student failed to complete." This would mean every non-HS student completed. The premises do not guarantee this; some non-HS students might also have missed the deadline. Hence (ii) is not certain. 

\[ \boxed{\text{Only (iii) follows with certainty } \Rightarrow \text{Option (D)}.} \]