Two 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: 1. All apples are mangoes. 2. Some bananas are mangoes. Conclusions: I. Some mangoes are bananas. II. Some mangoes are apples.
Understanding Syllogism Statements and Conclusions
This question involves logical reasoning, specifically syllogisms. We are given two statements and three conclusions and need to determine which conclusions logically follow from the given statements.
Analyzing the Syllogism Statements
Let's break down the two statements provided:
- Statement 1: All apples are mangoes.
- Statement 2: Some bananas are mangoes.
Statement 1 establishes a relationship where the entire set of 'apples' is included within the set of 'mangoes'. Statement 2 indicates an overlap between the set of 'bananas' and the set of 'mangoes'; there are some items that are both bananas and mangoes.
Evaluating the Syllogism Conclusions
Now, let's examine each conclusion based on the truth of the statements:
- Conclusion I: Some mangoes are bananas.
- Conclusion II: Some mangoes are apples.
- Conclusion III: No mango is an apple.
Detailed Evaluation of Each Conclusion
Let's analyze each conclusion individually:
Conclusion I: Some mangoes are bananas.
Statement 2 says, "Some bananas are mangoes". This means there is at least one banana that is also a mango. If there is at least one banana that is a mango, it logically follows that there is at least one mango that is a banana. This is a valid conversion of an 'I' type (Some...are...) statement. Therefore, Conclusion I logically follows from Statement 2.
Conclusion II: Some mangoes are apples.
Statement 1 says, "All apples are mangoes". This means every single apple is a mango. If all apples are mangoes, then the group of things that are apples is completely inside the group of things that are mangoes. This implies that the mangoes which are also apples exist. Therefore, it is true that 'Some mangoes are apples'. This is a valid deduction from an 'A' type (All...are...) statement. Therefore, Conclusion II logically follows from Statement 1.
Conclusion III: No mango is an apple.
Statement 1 tells us "All apples are mangoes". This directly means that all items belonging to the 'apple' category are also in the 'mango' category. This implies that the set of apples is a subset of the set of mangoes. Conclusion III, "No mango is an apple", states that there is no overlap whatsoever between mangoes and apples, meaning no mango is an apple and no apple is a mango. This contradicts Statement 1, which guarantees that all apples *are* mangoes, meaning there are definitely some mangoes (the ones that are apples) that are apples. Therefore, Conclusion III does not logically follow from the statements; in fact, it is inconsistent with Statement 1.
Summary of Conclusions
Based on our analysis:
- Conclusion I (Some mangoes are bananas) follows from Statement 2.
- Conclusion II (Some mangoes are apples) follows from Statement 1.
- Conclusion III (No mango is an apple) does not follow and contradicts Statement 1.
Thus, only conclusions I and II logically follow from the given statements.
Revision Table: Syllogism Basics
| Statement Type | Form | Conversion/Inference Example |
|---|---|---|
| A (Universal Affirmative) | All S are P | If All Apples are Mangoes, then Some Mangoes are Apples. |
| E (Universal Negative) | No S is P | If No Cat is a Dog, then No Dog is a Cat. |
| I (Particular Affirmative) | Some S are P | If Some Bananas are Mangoes, then Some Mangoes are Bananas. |
| O (Particular Negative) | Some S are not P | Conversion is not generally valid. |
Additional Information: Logical Reasoning and Inference
Logical reasoning questions, like syllogisms, test your ability to deduce conclusions from given premises (statements). The key is to only use the information provided in the statements, treating them as true regardless of real-world knowledge. Common types of inferences include conversion, where you swap the subject and predicate while maintaining validity for certain statement types (like 'All S are P' converting to 'Some P are S', or 'Some S are P' converting to 'Some P are S', or 'No S is P' converting to 'No P is S'). Combining statements can lead to further conclusions, but that wasn't necessary for Conclusions I and II in this problem.
Understanding the relationships established by "All", "Some", and "No" is crucial for solving syllogisms. "All S are P" means S is a subset of P. "Some S are P" means there's at least one S that is also P (an intersection). "No S is P" means the sets S and P are entirely separate.
Similar Questions
- All flowers are plants. Some plants are flowering plants. Which conclusion is logically valid?
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All coolers are robots.
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2. All principal are teachers.
3. Some principals are doctors.
Conclusions:
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Statements:
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2. All tables are beds.
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Conclusions:
I. No table is a chair.
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III. Some beds are tables.
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Statements:
1. No city is a district.
2. Some districts are zones.
3. Some zones are states.
Conclusions:
I. Some zones are districts.
II. Some districts are cities.
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Statements:
1. Some tables are chairs.
2. Some chairs are beds.
3. All beds are goods.
Conclusions:
I. Some chairs are goods.
Il. Some goods are not beds.
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Statements:
No man is engineer.
No engineer is driver.
Some drivers are shop-keepers.
Conclusions:
1. Some men are drivers.
2. No shop-keepers are engineer.
3. Some shop-keepers are not engineers.
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Statements:
All aero-planes are cars.
All helicopters are cars.
All cars are scooters.
Conclusions:
1. All helicopters are scooters.
2. Some aero-planes are helicopters.
3. No aero-plane is helicopter.
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Statements:
Some pillows are doors.
Some doors are beds.
Conclusions:
I. Some doors are pillows.
II. All beds are doors.
Important Questions from 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:
Some students are players.
All players are male.
Conclusions:
I. All males are players.
II. Some males are students.
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Statements:
No creative is an employer.
All experts are creative.
All workers are experts.
Conclusions:
I. No employer is an expert.
II. No worker is an employer.
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Some actors are choreographers.
All choreographers are producers.
Not a single producer is a director.
Conclusions:
I. Some actors are directors.
II. Not a single actor is a director.
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Statements :
1. All flowers are tulips.
2. No tulips are whites.
Conclusions :
I. All tulips are flowers.
II. Some tulips are whites.
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 rats are dogs.
Some rats are hens.
Conclusions:
I. Some rats are dogs.
II. Some hens are rats.
