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?
Statements and Conclusions Analysis
We need to determine which conclusion(s) logically follow from the given statements. Let's represent the statements and conclusions symbolically:
- Statement 1: All teachers are professors. (All T are P)
- Statement 2: No professor is a male. (No P are M)
- Statement 3: Some males are engineers. (Some M are E)
- Conclusion I: No engineer is a professor. (No E are P)
- Conclusion II: Some engineers are professors. (Some E are P)
- Conclusion III: No male is a teacher. (No M are T)
Evaluating Conclusions
Conclusion I: No engineer is a professor.
From Statement 2 (No P are M) and Statement 3 (Some M are E), we can infer that some engineers are males (Some E are M). Since no professor is male (Statement 2), these engineers who are males cannot be professors. Therefore, we can only conclude that some engineers are NOT professors. Conclusion I ('No engineer is a professor') is a much stronger claim and does not necessarily follow. Thus, Conclusion I is incorrect.
Conclusion II: Some engineers are professors.
As derived above, the statements only allow us to conclude that 'Some engineers are NOT professors'. We cannot logically infer that 'Some engineers ARE professors'. Thus, Conclusion II is incorrect.
Conclusion III: No male is a teacher.
Let's combine Statement 1 (All T are P) and Statement 2 (No P are M). This forms a valid syllogism. If every teacher is a professor, and no professor is a male, it logically follows that no teacher can be a male. This is equivalent to saying 'No male is a teacher'. Thus, Conclusion III is correct.
Final Determination
Based on the logical deduction:
- Conclusion I: Incorrect
- Conclusion II: Incorrect
- Conclusion III: Correct
Therefore, only Conclusion III can be logically inferred.
Correct Option Reasoning: Only conclusion III is correct.
Important Questions from Syllogism
- Consider the following sentences:
All benches are beds .No bed is a bulb. Some bulbs are lamps.
Which of the following can be inferred?
i. Some beds are lamps.
ii. Some lamps are beds. Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows.
Statements:
I. No manager is a leader.
II. All leaders are executives.
Conclusions:
I. No manager is an executive.
II. No executive is a manager.Given below are two statements 1 and 2, and two conclusions I and II.
Statement 1: All entrepreneurs are wealthy.
Statement 2: All wealthy are risk seekers.
Conclusion I: All risk seekers are wealthy.
Conclusion II: Only some entrepreneurs are risk seekers.
Based on the above statements and conclusions, which one of the following options is CORRECT?
Statements:
1. All heroes are winners.
2. All winners are lucky people.
Inferences:
I. All lucky people are heroes.
II. Some lucky people are heroes.
III. Some winners are heroes.
Which of the above inferences can be logically deduced from statements 1 and 2?Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world, it is given that the statement “Some human beings are not cruel creatures” is FALSE, then which of the following set of statement(s) can be logically inferred with certainty?
(i) All human beings are cruel creatures.
(ii) Some human beings are cruel creatures.
(iii) Some creatures that are cruel are human beings.
(iv) No human beings are cruel creatures.
