Statements: (i) Some teachers are advocates.
(ii) Some players are teachers.
Conclusions: (I) All players are advocates.
(II) All advocates are players.
(III) Some advocates are teachers.
Then which conclusion follows ?
Logical Reasoning Statements Analysis
This question requires us to analyze two given statements and determine which of the three provided conclusions logically follows from them. This is a typical syllogism problem testing deductive reasoning skills.
Statement Analysis
- Statement (i):
Some teachers are advocates.This statement establishes a relationship between the set of 'teachers' and the set of 'advocates'. It means there is at least one person who belongs to both categories. The overlap is confirmed, but it does not imply that *all* teachers are advocates, nor that *all* advocates are teachers. - Statement (ii):
Some players are teachers.Similarly, this statement establishes an overlap between the set of 'players' and the set of 'teachers'. It means there is at least one person who is both a player and a teacher. This does not provide information about whether *all* players are teachers or *all* teachers are players.
Conclusion Evaluation
Let's examine each conclusion based on the information from the statements:
- Conclusion (I):
All players are advocates.The statements tell us that some players are teachers (Statement ii) and some teachers are advocates (Statement i). However, the teachers who are players might be a completely different group from the teachers who are advocates. There's no information guaranteeing that every player must also be an advocate. Thus, this conclusion does not necessarily follow. - Conclusion (II):
All advocates are players.Similar to Conclusion (I), we only know about an overlap between teachers and advocates. We cannot infer that the entire group of advocates falls within the group of players. This conclusion does not necessarily follow. - Conclusion (III):
Some advocates are teachers.Statement (i) explicitly states, "Some teachers are advocates". In logic, this relationship is symmetric. If "Some A are B" is true, then "Some B are A" is also true. Therefore, if some teachers are advocates, it logically follows that some advocates must be teachers. This conclusion is valid based directly on Statement (i).
Valid Conclusion Identification
By analyzing the implications of the given statements, we find that only Conclusion (III) is logically guaranteed. Conclusions (I) and (II) make claims about entire sets (all players or all advocates) which cannot be supported by the "some" statements provided.
Therefore, the only conclusion that logically follows from the given statements is Only (III).
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.
