Three Statements are given followed by Four conclusions numbered I, II, III and IV. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: Some chairs are holders. Some holders are bottles. Some bottles are chairs. Conclusions: I. All chairs are bottles. II. All bottles are chairs. III. All holders are bottles. IV. All holders are chairs.
None of the conclusions follow.
Analyzing Syllogism Statements and Conclusions
This question asks us to evaluate four conclusions based on three given statements and determine which conclusions logically follow. We must assume the statements are true, regardless of common knowledge.
Understanding the Given Statements
The statements provide relationships between three categories: Chairs, Holders, and Bottles. All the statements use the quantifier 'Some', indicating a partial overlap between the categories.
- Some chairs are holders. (Represents a partial overlap between Chairs and Holders)
- Some holders are bottles. (Represents a partial overlap between Holders and Bottles)
- Some bottles are chairs. (Represents a partial overlap between Bottles and Chairs)
Evaluating the Given Conclusions
We need to examine each conclusion to see if it must be true based *only* on the information provided in the statements. The conclusions all use the quantifier 'All', which implies a complete inclusion of one category within another.
- All chairs are bottles. (Claims that every chair is also a bottle)
- All bottles are chairs. (Claims that every bottle is also a chair)
- All holders are bottles. (Claims that every holder is also a bottle)
- All holders are chairs. (Claims that every holder is also a chair)
Conclusion Validity Analysis
Let's analyze each conclusion based on the given 'Some' statements. Remember, 'Some A are B' means there is at least one A that is a B, but it does not give us information about 'All A' or 'All B'.
Conclusion I: All chairs are bottles.
The statements say "Some bottles are chairs" and "Some chairs are holders" and "Some holders are bottles". While there is an overlap between bottles and chairs (Statement 3), the statement "Some bottles are chairs" does not guarantee that *all* chairs are bottles. There could be chairs that are not bottles.
Therefore, Conclusion I does not logically follow from the statements.
Conclusion II: All bottles are chairs.
Similar to Conclusion I, Statement 3 says "Some bottles are chairs". This only tells us about a partial relationship. It does not mean that *all* bottles are chairs. There could be bottles that are not chairs.
Therefore, Conclusion II does not logically follow from the statements.
Conclusion III: All holders are bottles.
Statement 2 says "Some holders are bottles". This confirms that there is at least one holder that is a bottle. However, this statement does not tell us anything about the entire category of holders. There could be holders that are not bottles.
Therefore, Conclusion III does not logically follow from the statements.
Conclusion IV: All holders are chairs.
We have "Some chairs are holders" (Statement 1) and "Some holders are bottles" (Statement 2) and "Some bottles are chairs" (Statement 3). Combining 'Some' statements generally does not lead to an 'All' conclusion. From "Some chairs are holders" and "Some holders are bottles", we cannot conclude anything definite about the relationship between *all* holders and chairs. The statements only indicate partial overlaps. There could be holders that are neither chairs nor bottles, or holders that are bottles but not chairs, etc.
Therefore, Conclusion IV does not logically follow from the statements.
Summary of Conclusions
Based on the analysis, none of the four conclusions logically follow from the given statements. When all statements are of the 'Some' type, it is generally not possible to draw a definite 'All' conclusion.
| Conclusion | Analysis | Logically Follows? |
|---|---|---|
| I. All chairs are bottles. | 'Some bottles are chairs' does not imply 'All chairs are bottles'. | No |
| II. All bottles are chairs. | 'Some bottles are chairs' does not imply 'All bottles are chairs'. | No |
| III. All holders are bottles. | 'Some holders are bottles' does not imply 'All holders are bottles'. | No |
| IV. All holders are chairs. | 'Some' relationships do not guarantee 'All' relationships between these categories. | No |
Final Determination
Since none of the individual conclusions I, II, III, or IV logically follow from the statements, the correct option is the one stating that none of the conclusions follow.
Revision Table: Types of Syllogism Statements
| Type of Statement | Quantifier | Representation | Example |
|---|---|---|---|
| Universal Affirmative (A) | All | All S are P | All cats are mammals. |
| Universal Negative (E) | No | No S are P | No fish are birds. |
| Particular Affirmative (I) | Some | Some S are P | Some students are intelligent. |
| Particular Negative (O) | Some...not | Some S are not P | Some students are not intelligent. |
In this problem, all statements are of the 'Particular Affirmative' type (I).
Additional Information on Syllogisms
Syllogisms are a form of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true. The structure typically involves:
- A major premise (a general statement)
- A minor premise (a specific statement)
- A conclusion (derived from the premises)
In this question, we have three statements acting as premises. The conclusions are deductions we need to verify.
Key Rules and Concepts:
- If both premises are 'Some' statements, a definite 'All' conclusion cannot be drawn.
- A conclusion cannot be universal ('All' or 'No') if one of the premises is particular ('Some').
- A conclusion cannot contain a term that is not present in the premises (though this wasn't an issue in this specific question).
- The middle term (the term common to both premises, linking the other two) must be distributed in at least one premise to draw a universal conclusion between the other two terms. In 'Some' statements, terms are not distributed.
Understanding the distribution of terms in different statement types (A, E, I, O) is crucial for analyzing more complex syllogisms, but for this problem, recognizing that 'Some' premises don't support 'All' conclusions is sufficient.
Similar Questions
Two statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All teachers are engineers.
All clerks are teachers.
Conclusions:
I. Some engineers are clerks.
II. Some teachers are clerks.
III. Some clerks are not engineers.
Two statements are given followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All keys are locks.
All locks are handles.
Conclusions:
I. Some locks are keys.
II. Some handles are keys.
Three Statements are given followed by Three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All switches are fans.
No heater is a fan.
Some wires are heaters.
Conclusions:
I. Some wires are fans.
II. No switch is a heater.
III. No wire is a switch.
Three statements are given followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All H are G.
All V are H.
Some V are I.
Conclusions:
I. At least some G are I.
II. All I being H is a possibility.
Three Statements are given followed by Three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements :
Some beds are chairs.
Some chairs are tables.
All tables are cupboards.
Conclusions :
I. Some tables are beds.
II. Some cupboards are chairs.
III. Some cupboards are beds.
Read the given statement(s) 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 statement(s).
Statements :
Some ceilings are beds.
No bed is an apple.
All dogs are beds.
Conclusions :
I. Some ceilings being dogs is a possibility.
II. No dog is an apple.
III. All beds are dogs.
IV. No ceiling is an apple.
Two statements are given followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements :
All keys are locks.
All locks are handles.
Conclusions :
I. Some locks are keys.
II. All handles are keys.
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 fans are hammers.
All hammers are fishes.
Conclusions:
I. No fans are fishes.
II. Some fans are fishes.
Three statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All classrooms are schools.
No school is a park.
All houses are parks.
Conclusions:
I. No house is a classroom.
II. No park is a classroom.
III. No school is a house.
Read the given statements and conclusions carefully. Assuming that the information given in the statement 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 fans are coolers.
All coolers are equipment.
Some equipment are mobiles.
Conclusions:
I. Some equipments are fans.
II. Some mobiles are fans.
III. No equipment is fan and cooler both
Important Questions from Conventional Syllogism
In this question, three statements followed by two conclusions numbered I and II have been given. You have to take the given statements to be true even if they seem to be at variance from the commonly facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statements: Some flats are apartments.
No apartment is a hall.
Some halls are rooms.
Conclusions: I. At least some rooms are flats.
II. No apartment is a room.
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 blue are red.
II. Some green are red.
Conclusions:
I. No blue is green.
II. No red is green.
Given below are two statements, Consider these statements to be true even if they seem factuality absurd, Read the conclusions and then decide which of the given conclusions logically follow(s) from the given statements?
Statements :
1. All vases are flowers.
2. No flowers is a plant.
Conclusions :
1. No vases is a plant.
2. Some plant are vases
In the question two statements are given, followed by three conclusions, I, II and III. You have to consider the statements to be true even if it seems to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements.
Statement 1 : Some cars are scooters.
Statement 2 : All scooters are buses.
Conclusion I : Some scooters are cars.
Conclusion II : Some buses are cars.
Conclusion III : All cars are buses.
In the question below are given three statements followed by two conclusions. You have to take each of the given statements to be true. Read the conclusions and then decide which of the conclusions can be logically derived.
Statements:
Some schools are colleges.
No college is university.
All universities are hospitals.
Conclusions:
I. Some schools are universities.
II. At least some hospitals are colleges.
