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GATE 2022 CE (CE2) – Question 9

General Aptitude · Analytical Aptitude: Logical Reasoning and Deduction · 2 marks · Multiple choice

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?

  1. Only conclusion I is correct
  2. Either conclusion I or conclusion II is correct
  3. Either conclusion III or conclusion IV is correct
  4. Only conclusion I and conclusion III are correct

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Correct answer: (D) Only conclusion I and conclusion III are correct

Explanation

“Some soaps are clean” means the intersection of soaps and clean objects is nonempty; this immediately implies I. Because every clean object is wet, those same soaps are wet, establishing III.

II contradicts the nonempty intersection, and IV incorrectly extends a statement about some objects to all wet objects. **Answer: D, I and III**.