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?
- Only conclusion $\text{I}$ and conclusion $\text{II}$ are correct
- Only conclusion $\text{II}$ and conclusion $\text{III}$ are correct
- Only conclusion $\text{II}$ and conclusion $\text{IV}$ are correct
- Only conclusion $\text{III}$ and conclusion $\text{IV}$ are correct