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.
Only conclusion I and II follows
Understanding Syllogism Statements and Conclusions
This question asks us to analyze logical statements and determine which conclusions follow based on the given information. We are given two statements and three conclusions about the relationship between cars, scooters, and buses.
Given Statements:
- Statement 1: Some cars are scooters.
- Statement 2: All scooters are buses.
Given Conclusions:
- Conclusion I: Some scooters are cars.
- Conclusion II: Some buses are cars.
- Conclusion III: All cars are buses.
Analyzing the Conclusions:
Let's examine each conclusion based on the truth of the given statements. We can use Venn diagrams or logical rules to understand the relationships.
Analysis of Conclusion I: Some scooters are cars.
- Statement 1 says, "Some cars are scooters."
- This statement establishes a mutual relationship between cars and scooters. If some members of group A are members of group B, then it logically follows that some members of group B must also be members of group A. This is the converse of an 'Some' statement.
- Therefore, if "Some cars are scooters" is true, then "Some scooters are cars" must also be true.
- Conclusion I follows from Statement 1.
Analysis of Conclusion II: Some buses are cars.
- We know from Statement 1 that "Some cars are scooters."
- We know from Statement 2 that "All scooters are buses."
- Let's combine these two statements. There is a set of things that are both cars and scooters (from Statement 1). Since Statement 2 tells us that *every single* scooter is also a bus, the things that are both cars and scooters must also be buses.
- This means there is a set of things that are cars and are also buses. This logically leads to the conclusion "Some cars are buses."
- If "Some cars are buses" is true, then its converse, "Some buses are cars," is also true.
- Therefore, Conclusion II follows from Statements 1 and 2.
Analysis of Conclusion III: All cars are buses.
- Statement 1 says "Some cars are scooters." This means there might be some cars that are *not* scooters.
- Statement 2 says "All scooters are buses."
- Combining these, we know that the cars which *are* scooters are also buses (as shown for Conclusion II). However, we have no information about the cars that are *not* scooters. They might or might not be buses.
- Since we cannot confirm that *all* cars belong to the group of buses, we cannot conclude that "All cars are buses."
- Conclusion III does not follow from the statements.
Summary of Conclusions:
- Conclusion I: Some scooters are cars - Follows
- Conclusion II: Some buses are cars - Follows
- Conclusion III: All cars are buses - Does not follow
Based on our analysis, only Conclusion I and Conclusion II follow from the given statements.
Revision Table: Syllogism Analysis
Reviewing the types of statements and their implications:
| Statement Type | Example | Converse (follows if original true) |
|---|---|---|
| All A are B | All dogs are mammals. | Some B are A (Some mammals are dogs). |
| Some A are B | Some cats are black. | Some B are A (Some black things are cats). |
| No A is B | No fish are birds. | No B is A (No birds are fish). |
| Some A are not B | Some animals are not cats. | Does not necessarily follow (Some non-cats are animals - true by definition, but not converse). |
Additional Information: Syllogism Basics
Syllogisms are a type of logical argument where a conclusion is inferred from two or more statements (premises).
- Statements/Premises: These are the given facts, assumed to be true.
- Conclusion: This is the inference drawn from the statements.
- The goal is to determine which conclusions are logically necessary consequences of the statements.
- Common quantifiers used are "All", "Some", and "No".
- "Some" means at least one, and possibly all.
- Venn diagrams can be a helpful tool to visualize the relationships between categories described in the statements.
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 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 A are S.
II. No D is A.
Conclusions:
I. Some S are A.
II. All S are D.
III. No A is D.
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. Some land are hard.
II. No stone is land.
Conclusions:
I. Some hard are land.
II. Some stone are hard.
