Three statements are followed by three conclusions numbered I, II and III. You have to consider these statements to be true, even if they seem to be at variance with commonly known facts. Decide which of the given conclusions logically follow(s) from the given statements. Statements: All peacocks are pigeons. Some pigeons are pinks. Some pinks are birds. Conclusions: (I) Some pinks are peacocks. (II) Some birds are pigeons. (III) Some peacocks are birds.
None of the conclusion 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 based on those statements. In syllogism, we must accept the statements as true, even if they contradict common knowledge.
Analyzing the Given Statements
We have three statements involving different categories: Peacocks, Pigeons, Pinks, and Birds.
- All peacocks are pigeons.
- Some pigeons are pinks.
- Some pinks are birds.
Analyzing the Given Conclusions
We need to check if these conclusions can be definitely derived from the statements:
- Some pinks are peacocks.
- Some birds are pigeons.
- Some peacocks are birds.
Step-by-Step Analysis using Syllogism Rules or Venn Diagrams
Let's analyze each conclusion based on the relationships defined in the statements. We can visualize these relationships using Venn diagrams or apply the rules of syllogism.
Analysis of Conclusion I: Some pinks are peacocks.
- Statement 1 says All Peacocks (P) are Pigeons (Pi). This means the set of Peacocks is entirely inside the set of Pigeons (P ⊂ Pi).
- Statement 2 says Some Pigeons (Pi) are Pinks (PK). This means there is an overlap between the set of Pigeons and the set of Pinks.
- From these two statements (All P ⊂ Pi, Some Pi are PK), we cannot definitively say if the overlap of Pigeons and Pinks includes any Peacocks.
- The 'some pigeons' that are pinks could be the ones that are also peacocks, or they could be the ones that are not peacocks.
Consider an example:
| Category | Example 1 | Example 2 |
|---|---|---|
| Peacocks | {A} | {A} |
| Pigeons | {A, B} | {A, B} |
| Pinks | {B, C} | {A, C} |
In Example 1:
- All {A} are in {A, B} (Statement 1 holds).
- Some {A, B} (element B) are in {B, C} (Statement 2 holds).
- Are Some Pinks ({B, C}) Peacocks ({A})? No (B is not A, C is not A).
In Example 2:
- All {A} are in {A, B} (Statement 1 holds).
- Some {A, B} (element A) are in {A, C} (Statement 2 holds).
- Are Some Pinks ({A, C}) Peacocks ({A})? Yes (element A).
Since the conclusion "Some pinks are peacocks" is true in one scenario but false in another, it does not logically follow from the statements.
Analysis of Conclusion II: Some birds are pigeons.
- Statement 2 says Some Pigeons (Pi) are Pinks (PK). (Overlap Pi and PK)
- Statement 3 says Some Pinks (PK) are Birds (B). (Overlap PK and B)
- The structure "Some A are B, Some B are C" (Pi to PK, PK to B) does not guarantee any relationship between A and C (Pi and B).
Consider an example:
| Category | Example 1 | Example 2 |
|---|---|---|
| Pigeons | {1, 2} | {1, 2} |
| Pinks | {2, 3} | {2, 3} |
| Birds | {3, 4} | {3, 1} |
In Example 1:
- Some Pigeons ({1, 2} - element 2) are Pinks ({2, 3}) (Statement 2 holds).
- Some Pinks ({2, 3} - element 3) are Birds ({3, 4}) (Statement 3 holds).
- Are Some Birds ({3, 4}) Pigeons ({1, 2})? No (3 is not in {1, 2}, 4 is not in {1, 2}).
In Example 2:
- Some Pigeons ({1, 2} - element 2) are Pinks ({2, 3}) (Statement 2 holds).
- Some Pinks ({2, 3} - element 3) are Birds ({3, 1}) (Statement 3 holds).
- Are Some Birds ({3, 1}) Pigeons ({1, 2})? Yes (element 1).
Since the conclusion "Some birds are pigeons" is true in one scenario but false in another, it does not logically follow from the statements.
Analysis of Conclusion III: Some peacocks are birds.
- Statement 1: All Peacocks (P) are Pigeons (Pi). (P ⊂ Pi)
- Statement 2: Some Pigeons (Pi) are Pinks (PK). (Overlap Pi and PK)
- Statement 3: Some Pinks (PK) are Birds (B). (Overlap PK and B)
- We are looking for a link between Peacocks (P) and Birds (B).
- P is inside Pi. Pi overlaps PK. PK overlaps B.
- This chain of relationships does not guarantee any overlap between P and B.
Consider an example, combining previous ideas:
| Category | Example |
|---|---|
| Peacocks | {A} |
| Pigeons | {A, B} |
| Pinks | {B, C} |
| Birds | {C, D} |
In this example:
- All {A} are in {A, B} (Statement 1 holds).
- Some {A, B} (element B) are in {B, C} (Statement 2 holds).
- Some {B, C} (element C) are in {C, D} (Statement 3 holds).
- Are Some Peacocks ({A}) Birds ({C, D})? No (A is not in {C, D}).
Since we can construct a scenario where the statements are true but the conclusion "Some peacocks are birds" is false, it does not logically follow.
Conclusion Summary
Based on our analysis, none of the three conclusions (I, II, and III) can be logically derived from the given statements. It is possible to construct scenarios where the statements are true, but none of the conclusions hold.
Therefore, none of the conclusions follow.
Revision Table: Key Syllogism Concepts
| Statement Type | Relationship | Example |
|---|---|---|
| All A are B (Universal Affirmative) | A is a subset of B | All cats are animals. |
| No A are B (Universal Negative) | A and B are disjoint sets | No dogs are cats. |
| Some A are B (Particular Affirmative) | Overlap between A and B | Some students are athletes. |
| Some A are not B (Particular Negative) | Part of A is outside B | Some animals are not cats. |
Additional Information: Syllogism Rules and Fallacies
Syllogism problems test your ability to follow logical rules. When analyzing statements, remember:
- The word "some" in syllogism means "at least one". It does not exclude the possibility of "all".
- Conclusions must be necessarily true if the statements are true, not just possibly true.
- Chains of "some" statements do not guarantee a connection between the first and last terms (e.g., Some A are B, Some B are C, does NOT guarantee Some A are C).
- A universal statement (All or No) followed by a particular statement (Some) can sometimes lead to a particular conclusion, but the rules are specific.
- Always be careful with distribution of terms (whether a term refers to the entire category or just part of it).
Mastering syllogisms involves understanding these rules and practicing with different types of statements and combinations.
Similar Questions
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 reds are pinks.
All whites are pinks.
All pinks are oranges.
Conclusions:
I. All whites are oranges.
II. All oranges are reds.
III. Some oranges are whites.
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 M are A.
II. No A is R.
Conclusion:
I. No M is R.
II. Some A are M.
III. Some R are A.
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 c are f.
No f is t.
All p are c.
Conclusions:
I. Some t are c.
II. No p is t.
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 bottles are containers.
Some containers are buckets.
All buckets are soaps.
Conclusions:
I. Some soaps are bottles.
II. Some buckets are bottles.
III. Some soaps are containers.
In this question, 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 follows/follow from the statements.
Statements:
Some roses are yellow.
Some yellow are buses.
All buses are green.
Conclusions:
I. All yellow are roses.
II. Some buses are yellow.
III. All yellow are green.
Read the following statement carefully and identify the conclusion that follows.
Statement:
All plants are living beings. Some living beings are animals.Conclusions:
I. Some plants are animals.
II. All animals are plants.Three statements are given followed by three conclusions numbered I, Il and lII. 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 fruits are wines.
Some wines are juices.
All juices are alcohols.
Conclusions:
I. Some alcohols are juices.
Il. Some wines are alcohols.
III. Some wines are fruits.
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 R are M.
II. All L are M.
Conclusions:
I. Some M are not R.
II. Some L are R.
III. Some M are L.
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 laptops are phones.
Some phones are capsules.
Some capsules are pens.
Conclusions:
I. Some laptops are capsules.
II. Some phones are pens.
III. Some pens are capsules.
IV. Some pens are phones.
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 from the statements.
Statements:
All blocks are toys.
All toys are books.
All books are stories.
Conclusions:
I. Some toys are blocks.
II. Some blocks are books.
III. Some stories are toys.
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.
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.
Read the given statements and conclusions carefully. Assuming that the information in the statement is true even if they appear to be at variance with commonly known facts, choose the conclusion that logically follows from the statement beyond reasonable doubt.
Statement:-
1. Some dogs are cats.
2. All cats are birds.
Conclusion:-
1. Some dogs are birds.
2. No cat is dog.
In each question below are given three statements followed by two conclusions numbered I and II. You have to take the two/three given statements to be true even if they seem to be at variance from commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statement:
Some mobiles are laptops.
No laptop is computer.
All phones are computer.
Conclusion:
I. At least some mobiles are computer.
II. At least some phone are laptops.
