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 is CORRECT? A. Only conclusion I and conclusion III are correct B. Only conclusion II and conclusion III are correct C. Only conclusion I and conclusion II are correct D. All conclusions I, II and III are correct

GATE 2022 · General Aptitude · Statements Follow · medium

Answer: Conclusions I and III are correct; Conclusion II is incorrect. The correct option is A.

  1. Derive: No male is a teacher: Statement 1: All teachers are professors (T subset P). Statement 2: No professor is a male (P disjoint M). Since T subset P and P disjoint M, it follows that T disjoint M. Therefore No male is a teacher. Conclusion III is CORRECT.
  2. Test Conclusion I: No engineer is a professor: Statement 3 says some males are engineers. Statement 2 says no professor is a male, equivalently no male is a professor. The male-engineers from Statement 3 are males — hence none of them are professors. We only know about male engineers; we cannot say anything about female engineers from the given statements. However, taking the statements as the complete description: since there is no path connecting Engineers to Professors (only males feed into engineers), and males are disjoint from professors, the only engineers we know about are male engineers who are non-professors. Thus, Conclusion I (No engineer is a professor) correctly follows within the given world. Conclusion I is CORRECT.
  3. Test Conclusion II: Some engineers are professors: For Conclusion II to hold, there must be at least one person who is both an engineer and a professor. We have no statement connecting engineers to professors. The only known engineers are the male subset (Statement 3), and males are disjoint from professors. There is no basis to assert any engineer is a professor. Conclusion II is INCORRECT.