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.
Neither Conclusion I nor II is true
Analyzing Syllogism Statements and Conclusions
This question requires us to evaluate given statements and determine which of the provided conclusions logically follow based on those statements, disregarding commonly known facts. Let's break down the statements and conclusions.
Understanding the Given Statements
- Statement 1: Some flats are apartments. (Some F are A)
- Statement 2: No apartment is a hall. (No A is H)
- Statement 3: Some halls are rooms. (Some H are R)
Understanding the Conclusions to Evaluate
- Conclusion I: At least some rooms are flats. (Some R are F)
- Conclusion II: No apartment is a room. (No A is R)
We need to see if these conclusions necessarily follow from the statements. We can use Venn diagrams or logical deduction to analyze the relationships.
Analyzing the Relationships
Let's analyze the connections between the categories: Flats (F), Apartments (A), Halls (H), and Rooms (R).
- Statement 1 tells us there is an overlap between F and A.
- Statement 2 tells us there is absolutely no overlap between A and H. They are mutually exclusive.
- Statement 3 tells us there is an overlap between H and R.
We can see that Flats are connected to Apartments, Apartments are disconnected from Halls, and Halls are connected to Rooms. There is no direct connection stated between Flats and Halls, Flats and Rooms, or Apartments and Rooms. The "No A is H" statement creates a strong separation.
Evaluating Conclusion I: At least some rooms are flats. (Some R are F)
This conclusion claims there is an overlap between Rooms and Flats. Let's trace the relationships:
- F is related to A (Some F are A).
- A is NOT related to H (No A is H).
- H is related to R (Some H are R).
From these statements, we cannot establish a definite link between Flats and Rooms. While it's possible that some Flats could also be Rooms (depending on how the 'Some' overlaps work out and if there are elements outside the stated relationships), it is not a certainty. There is no information in the statements that *guarantees* an overlap between R and F. Since a conclusion must necessarily follow, Conclusion I does not logically follow.
Evaluating Conclusion II: No apartment is a room. (No A is R)
This conclusion claims there is absolutely no overlap between Apartments and Rooms. Let's look at the statements again:
- No apartment is a hall. (No A is H)
- Some halls are rooms. (Some H are R)
The second statement tells us there are some entities that are *both* Halls and Rooms. Let's call this set of entities H&R. From the first statement, we know that Apartments have *no* relationship with *any* Hall. This means Apartments also have no relationship with the entities in H&R (the rooms that are also halls).
However, the statement "Some halls are rooms" does not say that *all* rooms are halls. There might be rooms that are *not* halls. The statements provide no information about the relationship between Apartments and those Rooms that are *not* Halls. It is possible that some Apartments *are* Rooms (specifically, Rooms that are not Halls). Therefore, we cannot definitively conclude that "No apartment is a room". Conclusion II does not logically follow.
Summary of Findings
- Conclusion I (Some R are F) does not necessarily follow from the statements.
- Conclusion II (No A is R) does not necessarily follow from the statements.
Since neither conclusion is guaranteed to be true based on the given statements, the correct determination is that neither Conclusion I nor Conclusion II is true.
| Statements | Logical Representation |
|---|---|
| Some flats are apartments. | Some F are A |
| No apartment is a hall. | No A is H |
| Some halls are rooms. | Some H are R |
| Conclusions | Logical Representation | Follows? |
|---|---|---|
| At least some rooms are flats. | Some R are F | No |
| No apartment is a room. | No A is R | No |
Revision Table: Syllogism Rules Refresher
Understanding the basic types of statements and how they connect is crucial in syllogism problems.
| Statement Type | Relationship | Example | Inference Examples |
|---|---|---|---|
| All A are B | Universal Positive | All dogs are mammals. | If All A are B, then Some A are B, and Some B are A (if B exists). |
| No A is B | Universal Negative | No cat is a dog. | If No A is B, then No B is A, Some A are not B, and Some B are not A. |
| Some A are B | Particular Positive | Some students are tall. | If Some A are B, then Some B are A. No other definite conclusion follows between A and B. |
| Some A are not B | Particular Negative | Some students are not tall. | If Some A are not B, then no other definite conclusion follows between A and B. |
When combining statements, remember that two particular statements usually yield no definite conclusion. A negative statement and a particular statement also often yield no definite conclusion regarding the extremes. A 'No' relation between two terms often isolates them from conclusions involving terms linked only through them.
Additional Information: Syllogism Logic and Conclusion Types
Syllogism questions test your ability to deduce logical conclusions from given premises. It's important to remember:
- Truth vs. Logic: In syllogisms, the statements are assumed true, even if they contradict real-world facts. Your conclusions must follow *only* from the given statements.
- Definite Conclusions: A conclusion "follows" if it is *necessarily* true in all possible scenarios represented by the statements.
- Possibility vs. Certainty: If a conclusion *might* be true in some scenarios but not necessarily in all, it is a possibility, not a definite conclusion.
- Negative Statements: A negative statement ("No apartment is a hall") breaks the direct chain between the categories it relates. This break is significant when trying to connect other categories.
In this problem, the "No apartment is a hall" statement acts as a barrier, preventing a definite positive or negative link from being established between Flats (connected to Apartments) and Rooms (connected to Halls).
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:
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 following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. All A are S.
II. No D is A.
Conclusions:
I. Some S are A.
II. All S are D.
III. No A is D.
In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. Some land are hard.
II. No stone is land.
Conclusions:
I. Some hard are land.
II. Some stone are hard.
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.
