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.
All of the conclusions follow
Understanding Syllogism Statements and Conclusions
This question asks us to analyze a set of statements and determine which of the given conclusions logically follow from these statements. This type of problem is known as a Syllogism, a form of logical reasoning where a conclusion is drawn from two or more premises (statements).
Analyzing the Given Statements
We are given three statements:
- All classrooms are schools.
- No school is a park.
- All houses are parks.
We must assume these statements are true, even if they contradict general knowledge.
Representing the Statements Logically
We can represent these statements using set theory or simple diagrams to visualize the relationships:
- Statement 1: The set of 'Classrooms' is entirely contained within the set of 'Schools'. (Classroom $\subseteq$ School)
- Statement 2: The set of 'Schools' and the set of 'Parks' have no elements in common. They are disjoint sets. (School $\cap$ Park = $\emptyset$)
- Statement 3: The set of 'Houses' is entirely contained within the set of 'Parks'. (House $\subseteq$ Park)
Evaluating the Conclusions
Now let's evaluate each conclusion based on the relationships established by the statements.
Conclusion I: No house is a classroom.
Let's trace the connection between 'House' and 'Classroom' using the statements:
- Statement 3 tells us: All houses are parks.
- Statement 2 tells us: No school is a park.
If all houses are within the category of 'Parks', and the category of 'Parks' has absolutely no overlap with the category of 'Schools', then houses cannot be schools. So, 'No house is a school' is true.
- Statement 1 tells us: All classrooms are schools.
If houses cannot be schools (as derived above), and classrooms are a type of school (entirely inside schools), then houses also cannot be classrooms. There is no way for a house to be a classroom if houses cannot be schools at all.
Therefore, conclusion I, "No house is a classroom," logically follows from the statements.
Conclusion II: No park is a classroom.
Let's trace the connection between 'Park' and 'Classroom':
- Statement 1 tells us: All classrooms are schools.
- Statement 2 tells us: No school is a park.
If classrooms are a type of school (entirely inside schools), and the category of 'Schools' has absolutely no overlap with the category of 'Parks', then classrooms cannot be parks. If classrooms cannot be parks, then it is also true that no park is a classroom.
Therefore, conclusion II, "No park is a classroom," logically follows from the statements.
Conclusion III: No school is a house.
Let's trace the connection between 'School' and 'House':
- Statement 3 tells us: All houses are parks.
- Statement 2 tells us: No school is a park.
If all houses are within the category of 'Parks', and the category of 'Parks' has absolutely no overlap with the category of 'Schools', then houses cannot be schools. This means there is no common element between the sets 'School' and 'House'. If houses cannot be schools, then it is also true that no school is a house.
Therefore, conclusion III, "No school is a house," logically follows from the statements.
Summary of Conclusions
Based on our analysis:
- Conclusion I: No house is a classroom - Follows.
- Conclusion II: No park is a classroom - Follows.
- Conclusion III: No school is a house - Follows.
All three conclusions logically follow from the given statements.
| Conclusion | Logical Deduction | Follows? |
|---|---|---|
| I. No house is a classroom. | House $\subseteq$ Park, School $\cap$ Park = $\emptyset$ ∴ House $\cap$ School = $\emptyset$. Classroom $\subseteq$ School. If House $\cap$ School = $\emptyset$ and Classroom $\subseteq$ School, then House $\cap$ Classroom = $\emptyset$. | Yes |
| II. No park is a classroom. | Classroom $\subseteq$ School, School $\cap$ Park = $\emptyset$ ∴ Classroom $\cap$ Park = $\emptyset$. | Yes |
| III. No school is a house. | House $\subseteq$ Park, School $\cap$ Park = $\emptyset$ ∴ School $\cap$ House = $\emptyset$. | Yes |
Revision Table: Key Syllogism Concepts
| Concept | Explanation |
|---|---|
| Statement/Premise | A proposition assumed to be true for the purpose of the argument. |
| Conclusion | A judgment or decision reached by reasoning. Must logically follow from the statements. |
| Logical Following | A conclusion logically follows if it must be true whenever the statements are true. |
| Validity | A syllogism is valid if its conclusion necessarily follows from its premises. We are checking the validity of individual conclusions here. |
Additional Information on Syllogistic Reasoning
Syllogistic reasoning is a fundamental part of deductive logic. It involves drawing conclusions from general statements (premises) about categories or classes of things. The structure typically involves two premises and a conclusion. Common quantifiers used are "All", "No", and "Some".
When solving syllogism problems, it's important to:
- Read the statements carefully and accept them as true.
- Avoid using outside knowledge that contradicts the statements.
- Represent the relationships between categories using diagrams (like Venn diagrams) or logical notation.
- Systematically check if each conclusion is guaranteed to be true based *only* on the given statements.
If a conclusion is true in every possible scenario depicted by the statements, then it logically follows. If there is even one possible scenario where the conclusion is false while the statements are true, then the conclusion does not follow.
In this specific problem, the disjoint nature of 'School' and 'Park' combined with the subsets ('Classroom' within 'School', 'House' within 'Park') creates clear separations that support all three "No" conclusions.
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.
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.
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
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. All locks are keys.
II. All handles are keys.
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:
Some windows are doors.
No window is a cupboard.
Conclusions:
I. No cupboard is a door.
II. Some doors are definitely not cupboard.
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.
