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
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:
1. Some flowers are chemicals.
2. Some chemicals are herbs.
Conclusions:
I. No flower is a herb.
II. Some flowers are herbs.
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:
All students are teachers.
All teachers are professors.
Conclusions:
1. All students are professors.
2. All professors are students.
3. No teacher is a professor.
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 dentists are surgeons.
II. All the surgeons are doctors.
Conclusions:
I. Some dentists are doctors.
II. No surgeons are dentists.
The statements below are followed by two conclusions labelled I and II. Assuming that the information in the statements is true, even if it appears at variance with generally established facts. decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
1) Some angers are griefs.
2) Some griefs are loves.
Conclusion:
I. Some griefs are angers.
II. Some loves are griefsThe statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts. decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
Some cows are deer.
Some deer are fishes.
Conclusion:
I. Some cows are fishes.
II. Some fishes are cows.
