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: Only a few Bs are Qs. Only a few Qs are Vs. Conclusions: I. Some Bs are Vs. II. All Qs can never be Vs.
Only conclusion II follows.
Understanding Logical Reasoning Statements and Conclusions
This question asks us to analyze given statements and determine which of the provided conclusions logically follow. We must treat the statements as absolutely true, even if they contradict common knowledge.
Analyzing the Statements
The statements involve a specific type of relationship: "Only a few". Let's break down what this means.
- Statement 1: Only a few Bs are Qs.
- Statement 2: Only a few Qs are Vs.
The Meaning of "Only a few"
In logical reasoning problems, the phrase "Only a few A are B" implies two things:
- Some A are B.
- Some A are not B.
It also implies that some B are A, but the core constraint is on set A. Applying this to our statements:
- "Only a few Bs are Qs" means:
- Some Bs are Qs.
- Some Bs are not Qs.
- "Only a few Qs are Vs" means:
- Some Qs are Vs.
- Some Qs are not Vs.
Analyzing the Conclusions
Now let's examine each conclusion based on our understanding of the statements.
Conclusion I: Some Bs are Vs.
This conclusion suggests there is an overlap between the set of Bs and the set of Vs. Let's see if this must be true based on the statements:
- We know there is a relationship between B and Q, and between Q and V.
- Statement 1 tells us some Bs are Qs.
- Statement 2 tells us some Qs are Vs.
We can think of this using possibilities:
- Is it possible that the Qs that are Bs are completely separate from the Qs that are Vs? Yes, it is possible. The overlap between B and Q could be in one part of Q, and the overlap between Q and V could be in a completely different part of Q. In this case, there would be no overlap between B and V.
- Is it possible that some of the Qs that are Bs are also Qs that are Vs? Yes, it is also possible. This would create an overlap between B and V.
Since the conclusion "Some Bs are Vs" is possible but not guaranteed to be true in all valid scenarios based on the statements, it does not logically follow.
Conclusion II: All Qs can never be Vs.
This conclusion claims it is impossible for all Qs to be Vs. Let's look at Statement 2 again:
- Statement 2: Only a few Qs are Vs.
As we established, "Only a few Qs are Vs" explicitly means:
- Some Qs are Vs.
- Some Qs are not Vs.
If we know for certain that "Some Qs are not Vs", then it is absolutely impossible for "All Qs" to be Vs. There will always be that group of Qs that are not Vs.
Therefore, the conclusion "All Qs can never be Vs" logically follows directly from the meaning of the statement "Only a few Qs are Vs".
Summary of Conclusions
- Conclusion I: Some Bs are Vs - Does not follow.
- Conclusion II: All Qs can never be Vs - Follows.
Based on our analysis, only conclusion II follows from the given statements.
Revision Table: Key Concepts
| Statement Type | Implication 1 | Implication 2 |
|---|---|---|
| All A are B | Some A are B | No A are not B |
| No A are B | Some A are not B | Some B are not A |
| Some A are B | — | Possibility: Some A are not B, Some B are not A |
| Some A are not B | — | Possibility: Some A are B, Some B are A |
| Only a few A are B | Some A are B | Some A are not B |
Additional Information: The "Only a Few" Rule
The interpretation of "Only a few A are B" is crucial in modern logical reasoning questions. It is treated as a specific type of "some" statement that carries a strong implication of "some are not". Unlike a standard "Some A are B" (which allows for the possibility that all A are B), "Only a few A are B" strictly prohibits the possibility of "All A are B". This distinction is key to correctly solving problems involving this phrase, especially when dealing with conclusions about "All" or "Can never be". Always remember that "Only a few" sets a limit — it implies a partial relationship and denies a universal one.
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.
