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 is correct? A. Only conclusion I is correct B. Either conclusion I or conclusion II is correct C. Either conclusion III or conclusion IV is correct D. Both conclusions I and III are correct

GATE 2022 · General Aptitude · Statements Follow · medium

Answer: D. Both conclusions I and III are correct

1. Check Conclusion I: Some clean objects are soaps: Statement 1 says: exists x (soap(x) and clean(x)). This same x satisfies clean(x) and soap(x). So some clean objects are soaps. Conclusion I is TRUE.
2. Check Conclusion II: No clean object is a soap: Conclusion I proved that some clean object IS a soap. Conclusion II directly contradicts this. Conclusion II is FALSE.
3. Check Conclusion III: Some wet objects are soaps: From Step 1: exists x (soap(x) and clean(x)). Statement 2: forall x (clean(x) -> wet(x)). Applying Statement 2 to x: wet(x) is true. So x is both a soap and wet. Therefore some wet objects are soaps. Conclusion III is TRUE.
4. Check Conclusion IV: All wet objects are soaps: Statement 2 says all clean objects are wet, but wet objects can be many things — tap water, rain, etc. There is no premise that restricts all wet objects to being soaps. Conclusion IV is unsupported and FALSE.