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:
No bank is an office.
All offices are stalls.
Conclusions:
I. No bank is a stall.
II. No stall is a bank.
III. Some stalls are offices.
IV. All the stalls are offices
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 flowers are beautiful.
Vaidehi is beautiful.
Conclusions:
I. Vaidehi is a flower.
II. Some beautiful are flowers.
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. All rugs are blankets.
2. All blankets are pillows.
3. Some blankets are frames.
Conclusions:
I. All pillows are rugs.
II. Some pillows are rugs.
III. All rugs are frames
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 fingers are toes.
Some toes are rings.
Some rings are hands.
Conclusions:
I. Some hands are toes.
II. Some rings are fingers.
III. Some hands are fingers.
V. Some fingers are rings.
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 polygons are angles.
All angles are diagonals.
All cones are cubes.
All cubes are decagons.
No diagonal is a cube.
Conclusions:
I. Some diagonals are polygons.
II. All diagonals are decagons.
III. No polygon is a cone.
IV. Some cubes are angles.
