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.
Only conclusion 1 follows.
Understanding Syllogism Statements and Conclusions
This problem involves analyzing logical statements and determining which conclusions logically follow. This type of question is common in logical reasoning tests and is based on the principles of syllogism.
Analyzing the Given Statements
We are given two statements:
- Some dogs are cats.
- All cats are birds.
We must assume these statements are true, regardless of whether they align with real-world knowledge. Our task is to find what can be definitively concluded from these facts.
Analyzing the Given Conclusions
We need to evaluate two conclusions based on the statements:
- Some dogs are birds.
- No cat is dog.
Step-by-Step Logical Analysis
Evaluation of Conclusion 1: Some dogs are birds.
- Statement 1 tells us that there is an overlap between the group of dogs and the group of cats. Specifically, some members of the dog group are also members of the cat group.
- Statement 2 tells us that the entire group of cats is included within the group of birds. In other words, every single cat is also a bird.
- If we combine these two statements, consider the dogs that are cats (from Statement 1). Since all cats are birds (from Statement 2), these specific dogs (which are cats) must also be birds.
- Therefore, it logically follows that some dogs are birds. This conclusion is valid based on the given statements.
Evaluation of Conclusion 2: No cat is dog.
- Statement 1 explicitly states: "Some dogs are cats."
- The conclusion "No cat is dog" means that there is absolutely no overlap between the group of cats and the group of dogs.
- This directly contradicts Statement 1, which says there is an overlap (some dogs are cats, which implies some cats are dogs).
- Since the conclusion contradicts a given statement, it cannot logically follow from the statements.
Summary of Conclusion Analysis
Based on our analysis:
- Conclusion 1 (Some dogs are birds) logically follows from the statements.
- Conclusion 2 (No cat is dog) does not logically follow from the statements because it contradicts Statement 1.
Therefore, only Conclusion 1 follows.
Revision Table: Statements and Conclusions
| Statement/Conclusion | Content | Analysis | Follows? |
|---|---|---|---|
| Statement 1 | Some dogs are cats. | Premise | N/A |
| Statement 2 | All cats are birds. | Premise | N/A |
| Conclusion 1 | Some dogs are birds. | Logically derived from Statements 1 & 2 | Yes |
| Conclusion 2 | No cat is dog. | Contradicts Statement 1 | No |
Additional Information on Logical Syllogisms
Logical reasoning questions like this test your ability to understand deductive reasoning. A syllogism is a form of deductive reasoning where a conclusion is drawn from two or more premises (statements).
- Statements: These are the given facts or premises assumed to be true. They establish relationships between different categories (e.g., dogs, cats, birds).
- Conclusions: These are the inferences drawn from the statements. A conclusion is valid only if it MUST be true whenever the statements are true.
- Types of Statements: Common types include "All A are B," "No A is B," "Some A are B," and "Some A are not B." Understanding the relationship each type describes is key.
- Validity: A syllogism is valid if its conclusion follows logically from its premises. The truth of the conclusion in the real world is irrelevant; only the logical structure matters.
- Venn Diagrams: These can be a helpful visual tool to represent the relationships described in the statements and check if a conclusion is supported.
In this problem, the combination of "Some A are B" and "All B are C" often leads to "Some A are C." This is a standard inference pattern in syllogistic logic, applicable here to "Some dogs are cats" and "All cats are birds" concluding "Some dogs are birds."
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.
