Statements : Mohan is a good sportsman.
Sportsmen are healthy.
Conclusions : I. All healthy persons are sportsmen.
II. Mohan is healthy.
Which one of the following is correct?
This question involves logical reasoning based on given statements and conclusions.
Statement Analysis
- Statement 1: Mohan is a good sportsman.
- Statement 2: Sportsmen are healthy. This can be represented logically as: If someone is a sportsman, then they are healthy. ($\forall x (\text{Sportsman}(x) \implies \text{Healthy}(x))$)
Conclusion Analysis
- Conclusion I: All healthy persons are sportsmen. This is the converse of Statement 2 and does not necessarily follow. The fact that all sportsmen are healthy does not mean all healthy people must be sportsmen. ($\forall x (\text{Healthy}(x) \implies \text{Sportsman}(x))$)
- Conclusion II: Mohan is healthy. Since Mohan is a sportsman (Statement 1) and all sportsmen are healthy (Statement 2), it logically follows that Mohan must be healthy. ($\text{Sportsman}(\text{Mohan}) \land \forall x (\text{Sportsman}(x) \implies \text{Healthy}(x)) \implies \text{Healthy}(\text{Mohan})$)
Determining Correctness
- Conclusion I is incorrect because the relationship stated in Statement 2 cannot be reversed.
- Conclusion II is correct as it is a direct deduction from the given statements using basic logical inference (modus ponens).
Therefore, only Conclusion II follows from the given statements.
Important Questions from Conventional Syllogism
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
1. Some flowers are chemicals.
2. Some chemicals are herbs.
Conclusions:
I. No flower is a herb.
II. Some flowers are herbs.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
All students are teachers.
All teachers are professors.
Conclusions:
1. All students are professors.
2. All professors are students.
3. No teacher is a professor.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
I. Some dentists are surgeons.
II. All the surgeons are doctors.
Conclusions:
I. Some dentists are doctors.
II. No surgeons are dentists.
The statements below are followed by two conclusions labelled I and II. Assuming that the information in the statements is true, even if it appears at variance with generally established facts. decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
1) Some angers are griefs.
2) Some griefs are loves.
Conclusion:
I. Some griefs are angers.
II. Some loves are griefsThe statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts. decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
Some cows are deer.
Some deer are fishes.
Conclusion:
I. Some cows are fishes.
II. Some fishes are cows.
