Three statements are given, followed by four conclusions numbered I, II, III and IV. 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 birds are ducks. Some ducks are crows. All crows are parrots. Conclusions: I. Some parrots are birds. II. Some parrots are ducks. III. Some crows are birds. IV. All parrots are birds.
Only conclusion II follows
Analyzing Syllogism Statements and Conclusions
This problem requires us to analyze the given statements based on the principles of logical deduction and determine which of the conclusions logically follow. We must assume the statements are true, regardless of common knowledge.
Understanding the Syllogism Statements
We are given three statements:
- All birds are ducks. (This means the set of Birds is completely contained within the set of Ducks).
- Some ducks are crows. (This means there is at least one Duck that is also a Crow. The sets of Ducks and Crows overlap).
- All crows are parrots. (This means the set of Crows is completely contained within the set of Parrots).
To solve this, we can visualize these relationships using Venn diagrams or apply rules of syllogism. Let's consider the connections:
- Birds → Ducks (All Birds are Ducks)
- Ducks ↔ Crows (Some Ducks are Crows - implies Some Crows are Ducks)
- Crows → Parrots (All Crows are Parrots)
Combining these, we see a chain: Birds are part of Ducks, Ducks connect to Crows, and Crows are part of Parrots.
Evaluating Each Conclusion
Now, let's check each conclusion to see if it necessarily follows from the statements.
Conclusion I: Some parrots are birds.
We know All Birds are Ducks, Some Ducks are Crows, and All Crows are Parrots. From 'Some Ducks are Crows' and 'All Crows are Parrots', we can deduce 'Some Ducks are Parrots'. However, the Birds are only a subset of Ducks. The 'Some Ducks' that are Parrots might be the Ducks that are not Birds. Therefore, it is possible that no Birds are Parrots. This conclusion does not necessarily follow.
Conclusion II: Some parrots are ducks.
Look at the statements: 'Some ducks are crows' and 'All crows are parrots'. If some part of the Ducks set is also in the Crows set, and the entire Crows set is contained within the Parrots set, then that part of the Ducks set which is Crows must also be within the Parrots set. So, there must be some Ducks that are also Parrots. This means 'Some Ducks are Parrots' is true, which is equivalent to 'Some Parrots are Ducks'. This conclusion logically follows.
Conclusion III: Some crows are birds.
We have 'All birds are ducks' and 'Some ducks are crows'. Birds are inside Ducks. The overlap between Ducks and Crows ('Some ducks are crows') could occur entirely within the part of the Ducks that are not Birds. For example, if Ducks are represented by a large circle, Birds are a small circle inside it, and Crows overlap the large circle but only outside the small Birds circle. In this scenario, no Crows are Birds. Thus, this conclusion does not necessarily follow.
Conclusion IV: All parrots are birds.
We know 'All crows are parrots' and 'All birds are ducks'. For this conclusion to be true, the entire set of Parrots would need to be contained within the set of Birds. However, we know Crows are inside Parrots, and Crows only have a 'Some' relationship with Ducks, which contain Birds. It is clearly possible to have many Parrots (including all Crows) that are not Birds. This conclusion does not necessarily follow.
Summary of Conclusions
Based on the logical analysis of the statements:
- Conclusion I (Some parrots are birds): Does not follow.
- Conclusion II (Some parrots are ducks): Follows.
- Conclusion III (Some crows are birds): Does not follow.
- Conclusion IV (All parrots are birds): Does not follow.
Therefore, only conclusion II logically follows from the given statements.
| Statement | Relationship |
|---|---|
| All birds are ducks. | Birds ⊆ Ducks |
| Some ducks are crows. | Ducks ∩ Crows ≠ ∅ |
| All crows are parrots. | Crows ⊆ Parrots |
| Conclusion | Follows? | Reason |
|---|---|---|
| Some parrots are birds. | No | Possible scenario where no overlap exists between Birds and Parrots based on statements. |
| Some parrots are ducks. | Yes | From 'Some ducks are crows' and 'All crows are parrots', we get 'Some ducks are parrots', which means 'Some parrots are ducks'. |
| Some crows are birds. | No | Possible scenario where the 'Some ducks are crows' overlap is outside the 'Birds' subset of Ducks. |
| All parrots are birds. | No | Not necessarily true based on the given relationships; Crows are Parrots, and Crows may not overlap with Birds. |
Revision Table: Syllogism Basics
| Type | Relationship | Example |
|---|---|---|
| All A are B | A ⊆ B | If All Cats are Mammals, then the set of Cats is inside the set of Mammals. |
| Some A are B | A ∩ B ≠ ∅ | If Some Dogs are Brown, there is an overlap between the set of Dogs and the set of Brown things. |
| No A are B | A ∩ B = ∅ | If No Fish are Birds, the sets of Fish and Birds are separate. |
| Some A are not B | There exists A ∉ B | If Some Students are not Athletes, there is at least one student who is not in the set of Athletes. |
Additional Information: Syllogism and Logic
Syllogism is a form of logical reasoning where a conclusion is reached from two or more statements (premises). In these types of problems, the key is to determine what relationships are necessarily true based on the statements provided. Any conclusion that is merely possible, but not guaranteed in all valid interpretations of the statements, is considered not to follow. Venn diagrams are a helpful tool to visualize the relationships between the categories mentioned in the statements and test the validity of conclusions. Always remember to consider all possible valid diagrams that can be drawn from the statements.
Similar Questions
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
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.
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I. All T are G.
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Conclusions:
I. All T are H.
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III. All H are G.
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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 R are M.
II. All L are M.
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I. Some M are not R.
II. Some L are R.
III. Some M are L.
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:
Some bottles are towels.
No towel is a pillow.
All bottles are coats.
Conclusions:
I. Some coats are towels.
II. No coat is a towel.
III. Some bottles are pillows.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 Tim are Jack.
No Jack is Ben.
Some Ben is Ruth.
Conclusions:
I. No Ruth is Jack.
II. Some Ben are Jack.
III. No Ben is Tim.
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.
- Sunita travels 6 Km towards north east. Then travels 9 Km towards west. From there, she goes 6 Km south-west and finally goes 3 Km towards east. How far is she from her initial position?
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.
