GATE EE 2023 Set 1 — Question 6
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General Aptitude → Analytical Aptitude → Deduction & Induction
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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. However, by the time the due date for registration was over, it was found that suprisingly 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) 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.
(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.
Correct answer
(D) only (iii)
Solution
Let be the set of students who completed registration, be the set of eligible voters, and be the set of students from the Department of Human Sciences.
Premise 1: (Registered students are eligible).
Premise 2: (No Human Sciences student is registered).Analysis of statements:
(i) : This says all ineligible students are from Human Sciences. This is not necessarily true; students from other departments might also have failed to register.
(ii) : This says all students not in Human Sciences are registered. This is not necessarily true; some might have missed the deadline.
(iii) : This says all eligible voters are not from Human Sciences. Since and , it follows that , which means . This is logically certain.Therefore, only statement (iii) can be inferred with certainty.
Premise 1: (Registered students are eligible).
Premise 2: (No Human Sciences student is registered).Analysis of statements:
(i) : This says all ineligible students are from Human Sciences. This is not necessarily true; students from other departments might also have failed to register.
(ii) : This says all students not in Human Sciences are registered. This is not necessarily true; some might have missed the deadline.
(iii) : This says all eligible voters are not from Human Sciences. Since and , it follows that , which means . This is logically certain.Therefore, only statement (iii) can be inferred with certainty.
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