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:
No bank is an office.
All offices are stalls.
Conclusions:
I. No bank is a stall.
II. No stall is a bank.
III. Some stalls are offices.
IV. All the stalls are offices
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 flowers are beautiful.
Vaidehi is beautiful.
Conclusions:
I. Vaidehi is a flower.
II. Some beautiful are flowers.
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. All rugs are blankets.
2. All blankets are pillows.
3. Some blankets are frames.
Conclusions:
I. All pillows are rugs.
II. Some pillows are rugs.
III. All rugs are frames
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:
Some fingers are toes.
Some toes are rings.
Some rings are hands.
Conclusions:
I. Some hands are toes.
II. Some rings are fingers.
III. Some hands are fingers.
V. Some fingers are rings.
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 polygons are angles.
All angles are diagonals.
All cones are cubes.
All cubes are decagons.
No diagonal is a cube.
Conclusions:
I. Some diagonals are polygons.
II. All diagonals are decagons.
III. No polygon is a cone.
IV. Some cubes are angles.
