Students of all the departments of a college who have successfully completed the registration process are eligible to vote in the upcoming college elections. However, by the time the due date for registration was over, it was found that surprisingly none of the students from the Department of Human Sciences had completed the registration process. Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty? i. All those students who would not be eligible to vote in the college elections would certainly belong to the Department of Human Sciences. ii. 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)

GATE 2023 · General Aptitude · Logical Reasoning · medium

Answer: D. Only (iii)

1. Formalise the given facts: Let R(x) = x completed registration, E(x) = x is eligible, HS(x) = x is a Human Sciences student. Fact 1: R(x) -> E(x) (registered implies eligible). Fact 2: forall x, HS(x) -> not R(x) (no HS student registered).
2. Evaluate statement iii: iii claims: E(x) -> not HS(x). From step 1, HS(x) -> not E(x). Contrapositive: E(x) -> not HS(x). This matches iii exactly — CERTAIN.
3. Evaluate statement i: i claims: not E(x) -> HS(x). We know HS(x) -> not E(x), but the converse (not E(x) -> HS(x)) does not follow. Students from other departments might also be ineligible (if they failed to register for other reasons).
4. Evaluate statement ii: ii claims students from other departments failed to register. The passage gives no information about non-HS registration success. This is beyond the given data — NOT certain.