​​​​​​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?

1. Only conclusion $\text{III}$ is correct
2. Only conclusion $\text{I}$ and conclusion $\text{II}$ are correct
3. Only conclusion $\text{II}$ and conclusion $\text{III}$ are correct
4. Only conclusion $\text{I}$ and conclusion $\text{III}$ are correct

Given that,

• Statement $1$: All teachers are professors.
• Statement $2$: No professor is a male.
• Statement $3$: Some males are engineers.

We can draw the Venn diagram using the above statements.

Now, we can conclude from the above two Venn diagrams.

• Conclusion $\text{I}$: No engineer is a professor. ${\color{Red}{-\text{False}}}$
• Conclusion $\text{II}$: Some engineers are professors.${\color{Red}{-\text{False}}}$
• Conclusion $\text{III}$: No male is a teacher.${\color{Green}{-\text{True}}}$

Correct Answer $:\text{A}$

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