GATE CS 2022 Set 1 — Question 4

MCQ+1 / -0.33EasyDeduction & InductionAnalytical AptitudeGeneral Aptitude

General Aptitude → Analytical Aptitude → Deduction & Induction

Last updated 5 September 2026

Question

Given below are four statements. Statement 1: All students are inquisitive. Statement 2: Some students are inquisitive. Statement 3: No student is inquisitive. Statement 4: Some students are not inquisitive. From the given four statements, find the two statements that CANNOT BE TRUE simultaneously, assuming that there is at least one student in the class.

Correct answer (A) Statement 1 and Statement 3 Solution We analyze the statements using the Square of Opposition in logic: Statement 1 (A): All students are inquisitive. Statement 2 (I): Some students are inquisitive. Statement 3 (E): No student is inquisitive. Statement 4 (O): Some students are not inquisitive. Analysis of pairs: Statement 1 and Statement 3: These are contrary statements. If "All" is true, "None" must be false. If "None" is true, "All" must be false. They cannot both be true at the same time (though both can be false). Thus, they cannot be true simultaneously . Statement 1 and Statement 2: If "All" is true, "Some" is necessarily true (subalternation). They can be true simultaneously. Statement 2 and Statement 4: "Some are" and "Some are not" are sub-contraries. They can both be true simultaneously (e.g., if the class is mixed). Statement 3 and Statement 4: If "No student is inquisitive" is true, then it implies "Some students are not inquisitive". They can be true simultaneously. Therefore, Statement 1 and Statement 3 cannot be true simultaneously. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer (A) Statement 1 and Statement 3 Solution We analyze the statements using the Square of Opposition in logic: Statement 1 (A): All students are inquisitive. Statement 2 (I): Some students are inquisitive. Statement 3 (E): No student is inquisitive. Statement 4 (O): Some students are not inquisitive. Analysis of pairs: Statement 1 and Statement 3: These are contrary statements. If "All" is true, "None" must be false. If "None" is true, "All" must be false. They cannot both be true at the same time (though both can be false). Thus, they cannot be true simultaneously . Statement 1 and Statement 2: If "All" is true, "Some" is necessarily true (subalternation). They can be true simultaneously. Statement 2 and Statement 4: "Some are" and "Some are not" are sub-contraries. They can both be true simultaneously (e.g., if the class is mixed). Statement 3 and Statement 4: If "No student is inquisitive" is true, then it implies "Some students are not inquisitive". They can be true simultaneously. Therefore, Statement 1 and Statement 3 cannot be true simultaneously.

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