GATE Civil 2022 Set 2 | GA Question: 9

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 $\text{I}$: Some clean objects are soaps.

Conclusion $\text{II}$: No clean object is a soap.

Conclusion $\text{III}$: Some wet objects are soaps.

Conclusion $\text{IV}$: All wet objects are soaps.

Which one of the following options can be logically inferred?

• A. Only conclusion $\text{I}$ is correct
• B. Either conclusion $\text{I}$ or conclusion $\text{II}$ is correct
• C. Either conclusion $\text{III}$ or conclusion $\text{IV}$ is correct
• D. Only conclusion $\text{I}$ and conclusion $\text{III}$ are correct

Answer 1

Given the statements:

• Statement $1:$ Some soaps are clean.

• Statement $2:$ All clean objects are wet.

Based on the above two statements we can draw the Venn diagram.

Now, we can conclude that, based on the above two Venn diagrams.

• Conclusion I: Some clean objects are soaps. ${\color{Green}{-\text{True}}}$
• Conclusion II: No clean object is a soap.${\color{Red}{-\text{False}}}$
• Conclusion III: Some wet objects are soaps.${\color{Green}{-\text{True}}}$
• Conclusion IV: All wet objects are soaps.${\color{Red}{-\text{False}}}$

$\therefore$ Only conclusion I or conclusion III are correct.

Correct Answer $:\text{D}$