GATE Electrical 2022 | GA Question: 4

Question

Given below are two statements and four conclusions drawn based on the statements.

Statement $1$: Some bottles are cups.

Statement $2$: All cups are knives.

 

Conclusion $\text{I}$ : Some bottles are knives.

Conclusion $\text{II}$ : Some knives are cups.

Conclusion $\text{III}$ : All cups are bottles.

Conclusion $\text{IV}$ : All knives are cups.

Which one of the following options can be logically inferred?

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

Answer 1

Given that, 

• $\text{Statement 1} :$ Some bottles are cups.

• $\text{Statement 2} :$ All cups are knives. 

Now, we can make a conclusion based on the above two Venn diagrams.

• $\text{Conclusion I}:$ Some bottles are knives ${\color{Green}{-\text{True.}}}$
• $\text{Conclusion II}:$ Some knives are cups ${\color{Green}{-\text{True.}}}$
• $\text{Conclusion III}:$ All cups are bottles ${\color{Red}{-\text{False.}}}$
• $\text{Conclusion IV}:$ All knives are cups ${\color{Red}{-\text{False.}}}$

Correct Answer $:\text{A}$