GATE CE 2022 Set 2 — Question 9

MCQ+2 / -0.67EasyDeduction & InductionAnalytical AptitudeGeneral Aptitude

General Aptitude → Analytical Aptitude → Deduction & Induction

Last updated 5 September 2026

Question

Given below are two statements and four conclusions drawn based on the statements. Statement 1: Some soaps are clean. Statement 2: All clean objects are wet. Conclusion I: Some clean objects are soaps. Conclusion II: No clean object is a soap. Conclusion III: Some wet objects are soaps. Conclusion IV: All wet objects are soaps. Which one of the following options can be logically inferred?

Correct answer (D) Only conclusion I and conclusion III are correct Solution Let's analyze the statements using Venn diagrams or logical deduction: Statement 1: Some soaps are clean. (Intersection between Soaps and Clean objects exists). Statement 2: All clean objects are wet. (The set of Clean objects is a subset of the set of Wet objects). Evaluating Conclusions: Conclusion I: Some clean objects are soaps. Since 'Some soaps are clean', it logically follows that 'Some clean objects are soaps'. This is the converse of Statement 1. (Correct) Conclusion II: No clean object is a soap. This contradicts Statement 1. (Incorrect) Conclusion III: Some wet objects are soaps. From Statement 1, there is an intersection between Soaps and Clean objects. From Statement 2, all Clean objects are Wet. Therefore, the soaps that are clean must also be wet. Thus, some wet objects are soaps. (Correct) Conclusion IV: All wet objects are soaps. While some wet objects are soaps, we cannot conclude that all wet objects are soaps based on the given information. (Incorrect) Conclusions I and III are logically correct. Therefore, the correct option is (D). Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer (D) Only conclusion I and conclusion III are correct Solution Let's analyze the statements using Venn diagrams or logical deduction: Statement 1: Some soaps are clean. (Intersection between Soaps and Clean objects exists). Statement 2: All clean objects are wet. (The set of Clean objects is a subset of the set of Wet objects). Evaluating Conclusions: Conclusion I: Some clean objects are soaps. Since 'Some soaps are clean', it logically follows that 'Some clean objects are soaps'. This is the converse of Statement 1. (Correct) Conclusion II: No clean object is a soap. This contradicts Statement 1. (Incorrect) Conclusion III: Some wet objects are soaps. From Statement 1, there is an intersection between Soaps and Clean objects. From Statement 2, all Clean objects are Wet. Therefore, the soaps that are clean must also be wet. Thus, some wet objects are soaps. (Correct) Conclusion IV: All wet objects are soaps. While some wet objects are soaps, we cannot conclude that all wet objects are soaps based on the given information. (Incorrect) Conclusions I and III are logically correct. Therefore, the correct option is (D).

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