Question

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 I: No engineer is a professor.
Conclusion II: Some engineers are professors.
Conclusion III: No male is a teacher.
Which one of the following options can be logically inferred?

• A. Only conclusion III is correct
• B. Only conclusion I and conclusion II are correct
• C. Only conclusion II and conclusion III are correct
• D. Only conclusion I and conclusion III are correct

Hint:

To analyze logical conclusions, carefully examine the given statements and see how they restrict or support the conclusions.

Answer 1

The Correct Option is A

Step 1: Analyze Statement 1 and Statement 2.
Statement 1 says that all teachers are professors, meaning that every teacher is also a professor.
Statement 2 says that no professor is male, which means that all professors are female.
Step 2: Examine Conclusion I.
Conclusion I states that no engineer is a professor.
Since Statement 2 asserts that all professors are female and Statement 3 says that some males are engineers, we cannot infer that engineers and professors are mutually exclusive. Therefore, Conclusion I is incorrect.
Step 3: Examine Conclusion II.
Conclusion II states that some engineers are professors.
Since Statement 2 declares that no professor is male and Statement 3 states that some males are engineers, we cannot infer that engineers can also be professors. Therefore, Conclusion II is incorrect.
Step 4: Examine Conclusion III.
Conclusion III states that no male is a teacher.
From Statement 2, which says that no professor is male, we can infer that no male can be a teacher because all teachers are professors. Therefore, Conclusion III is correct.
Final Answer: \[ \boxed{A} \]