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 conclusion logically follow(s) from the statements. Statements: No photographer is an architect. All engineers are photographers. All postmen are architects. Conclusions: I. No engineer is an architect. II. No engineer is a postman. III. No photographer is a postman.
All conclusions follow
Solving the Syllogism Problem
This problem involves analyzing logical statements and determining which conclusions can be drawn from them. We are given three statements and three conclusions. We must assume the statements are true and check which conclusions logically follow.
Understanding the Statements
Let's represent the categories using letters:
- P: Photographers
- A: Architects
- E: Engineers
- M: Postmen
The statements can be written as:
- No photographer is an architect. (P and A are disjoint sets: \(P \cap A = \emptyset\))
- All engineers are photographers. (E is a subset of P: \(E \subseteq P\))
- All postmen are architects. (M is a subset of A: \(M \subseteq A\))
Analyzing the Conclusions
Let's examine each conclusion based on the given statements.
Conclusion I: No engineer is an architect.
- Statement 2 tells us that all engineers are photographers (\(E \subseteq P\)).
- Statement 1 tells us that no photographer is an architect (\(P \cap A = \emptyset\)).
- If all engineers are a part of the group 'photographers', and the group 'photographers' has no members in common with the group 'architects', then the group 'engineers' can also have no members in common with the group 'architects'.
- Therefore, no engineer is an architect logically follows.
Conclusion II: No engineer is a postman.
- From Conclusion I, we established that no engineer is an architect (\(E \cap A = \emptyset\)).
- Statement 3 tells us that all postmen are architects (\(M \subseteq A\)).
- If no engineer is an architect, and all postmen are a part of the group 'architects', then no engineer can be a postman.
- Therefore, no engineer is a postman logically follows.
Conclusion III: No photographer is a postman.
- Statement 1 tells us that no photographer is an architect (\(P \cap A = \emptyset\)).
- Statement 3 tells us that all postmen are architects (\(M \subseteq A\)).
- If no photographer is an architect, and all postmen are a part of the group 'architects', then no photographer can be a postman.
- Therefore, no photographer is a postman logically follows.
Summary of Conclusions
| Conclusion | Logical Follows? | Reasoning |
|---|---|---|
| I. No engineer is an architect. | Yes | Engineers are Photographers, Photographers are not Architects. |
| II. No engineer is a postman. | Yes | Engineers are not Architects, Postmen are Architects. |
| III. No photographer is a postman. | Yes | Photographers are not Architects, Postmen are Architects. |
Based on the analysis of each conclusion, all three conclusions logically follow from the given statements.
Revision Table: Syllogism Basics
| Term | Explanation | Example (from this problem) |
|---|---|---|
| Statement | A premise assumed to be true for the purpose of logic. | "All engineers are photographers." |
| Conclusion | A judgment or decision reached by reasoning. | "No engineer is an architect." |
| Syllogism | A form of reasoning where a conclusion is drawn from two or more premises. | The entire problem structure. |
| Disjoint Sets | Sets that have no elements in common. | Photographers and Architects (Statement 1). |
| Subset | A set where every element is also an element of a larger set. | Engineers are a subset of Photographers (Statement 2). |
Additional Information: Solving Syllogisms
Solving syllogism problems requires careful attention to the logical relationships between different categories mentioned in the statements. Two common methods are:
- Venn Diagrams: Drawing overlapping or separate circles to represent the sets (categories) and shading regions based on the statements. This provides a visual way to see the relationships and check if a conclusion is supported by the diagram.
- Logical Deduction: Using rules of logic to combine statements and derive new valid conclusions. This involves understanding terms like "all," "some," "no," and how they affect set relationships (subset, intersection, disjoint).
It is crucial to remember that in syllogisms, you must accept the statements as true, even if they contradict real-world knowledge. The validity of a conclusion depends solely on whether it logically follows from the given statements, not on its factual correctness in reality.
Similar Questions
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 parks are hospitals.
Some hospitals are schools.
Some schools are colleges.
Conclusions:
I. Some parks are colleges.
II. All hospitals are schools.
III. No park is a college
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 parrots are pigs.
Some pigs are poles.
All poles are pets.
Conclusions:
I. Some poles are pigs.
II. Some pets are parrots.
III. All the parrots are pets.
IV. Some pets are pigs.
Three statements are given, followed by three conclusions I, II and III. Considering the statements to be true, even if they seem to be at variance from commonly known facts, decide which conclusion(s) logically follows from the statements.
Statement :
All schools are colleges.
All colleges are houses.
All houses are roads.
Conclusion :
I. All schools are roads.
II. All schools are houses.
III. All colleges are roads.
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 cribs are pants.
No crib is a tap.
All pants are shells.
Conclusions:
I. All shells being cribs is a possibility.
II. At least some taps are not cribs.
III. Some pants are not taps.
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 computers are footballs.
Some footballs are round.
Some round are stools.
Conclusions:
I. Some footballs are computers.
II. Some round are footballs.
III. Some stools are round.
Three statements are given followed by three conclusions I, II and III. Assuming that the information given in the statements is true, even if it seems to be at variance with commonly known facts, decide which of the given conclusions logically follows from the statements.
Statement :
No mug is bucket.
All mugs are cups.
Some cups are spoons.
Conclusion:
I. Some spoons are buckets.
II. Some mugs are spoons.
III. Some cups are not buckets.
Given below are three statements followed by three conclusions I, II and III. Considering the statements to be true, even if they seem to be at variance from commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statement :
All tanks are plates.
All cots are plates.
Some oats are cots.
Conclusion:
I. Some tanks are cots.
II. Some plates are tanks.
III. Some plates are oats.
Three statements are followed by three conclusions numbered I, II and III. You have to consider these statements to be true even if they seem to be at variance from commonly known facts. Decide which conclusion(s) logically follows from the given statements.
Statement :
No Pigeon is a Panduk.
Some Panduk are sparrows.
All sparrows are birds.
Conclusion:
(I) Some sparrows are not pigeons.
(II) Some sparrows are Panduk.
(III) Some birds are Panduk.
Three statements are followed by three conclusions numbered I, II and III. You have to consider these statements to be true, even if they seem to be at variance with commonly known facts. Decide which of the given conclusions logically follow(s) from the given statements.
Statements:
All bottles are plastics.
Some plastics are fibres.
Some fibres are glasses.
Conclusions:
(I) Some fibres are plastics.
(II) All plastics are bottles.
(III) Some glasses are fibres.
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 diamonds are stones.
Some stones are hard.
All hard are rocks.
Conclusions:
I. Some stones are diamonds.
II. All stones are hard.
III. Some hard are rocks.
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.
