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
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.- Given below are four statements.
Statement 1: All students are inquisitive.
Statement 2: Some students are inquisitive.
Statement 3: No student is inquisitive.
Statement 4: Some students are not inquisitive.
From the given four statements, find the two statements that CANNOT BE TRUE simultaneously, assuming that there is at least one student in the class. - Based only on the truth of the statement ‘Some humans are intelligent', which one of the following options can be logically inferred with certainty?
Given below are two statements and four conclusions drawn based on the statements.
Statement 1: Some bottles are cups.
Statement 2: All cups are knives.
Conclusion I: Some bottles are knives.
Conclusion II: Some knives are cups.
Conclusion III: All cups are bottles.
Conclusion IV: All knives are cups.
Which one of the following options can be logically inferred?
