Given below are three conclusions drawn based on the following three statements.
Statement $1$ : All teachers are professors.
Statement $2$ : No professor is a male.
Statement $3$ : Some males are engineers.
Conclusion $\text{I}$: No engineer is a professor.
Conclusion $\text{II}$: Some engineers are professors.
Conclusion $\text{III}$: No male is a teacher.
Which one of the following options can be logically inferred?
- Only conclusion $\text{III}$ is correct
- Only conclusion $\text{I}$ and conclusion $\text{II}$ are correct
- Only conclusion $\text{II}$ and conclusion $\text{III}$ are correct
- Only conclusion $\text{I}$ and conclusion $\text{III}$ are correct