Read the given statements and conclusions carefully. Assuming that the information given in the statements is ture, 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: 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.
Only conclusion 3 follows.
Analyzing Statements and Conclusions Logic
Let's break down the given statements and conclusions to determine which conclusions logically follow from the statements.
The Statements:
- No man is engineer.
- No engineer is driver.
- Some drivers are shop-keepers.
The Conclusions:
- Some men are drivers.
- No shop-keepers are engineer.
- Some shop-keepers are not engineers.
Evaluating Each Conclusion:
Conclusion 1: Some men are drivers.
The first statement says "No man is engineer". This means the set of men and the set of engineers are completely separate.
The second statement says "No engineer is driver". This means the set of engineers and the set of drivers are also completely separate.
From these two statements, we know that Engineers are separate from Men and Engineers are separate from Drivers. However, the statements provide no direct information about the relationship between Men and Drivers. There is no logical connection established between these two categories through the common term 'engineer'. Therefore, we cannot conclude that "Some men are drivers". This conclusion does not logically follow from the statements.
Conclusion 2: No shop-keepers are engineer.
The second statement says "No engineer is driver". This means engineers and drivers have no individuals in common. All engineers are not drivers, and all drivers are not engineers.
The third statement says "Some drivers are shop-keepers". This means there is at least one individual who is both a driver and a shop-keeper. Let's call this group 'Driver-Shop-keepers'.
We know that 'No engineer is driver'. This implies that any person who is a driver cannot be an engineer. Since the 'Driver-Shop-keepers' are a part of the drivers, it means the 'Driver-Shop-keepers' cannot be engineers.
This tells us that the shop-keepers who are also drivers are definitely not engineers. This supports Conclusion 3 ("Some shop-keepers are not engineers"). However, Statement 3 only talks about *some* drivers being shop-keepers. It doesn't say *all* shop-keepers are drivers. There might be other shop-keepers who are not drivers. The statements do not give us any information about whether these non-driver shop-keepers can be engineers or not (though Statement 1 rules out *men* being engineers, it doesn't rule out others). To conclude "No shop-keepers are engineer" (a universal negative), we would need to show that *all* shop-keepers cannot be engineers. The given statements do not provide enough information to support this universal claim. Therefore, Conclusion 2 does not necessarily follow.
Conclusion 3: Some shop-keepers are not engineers.
Let's use the same reasoning as for Conclusion 2.
Statement 3: "Some drivers are shop-keepers". This identifies a group of people who are both drivers and shop-keepers.
Statement 2: "No engineer is driver". This confirms that the set of engineers and the set of drivers are disjoint. If someone is a driver, they cannot be an engineer.
Consider the group of people who are "Some drivers are shop-keepers". These individuals are drivers. Since they are drivers, and we know "No engineer is driver", these individuals cannot be engineers. These individuals are also shop-keepers (by definition of "Some drivers are shop-keepers"). Therefore, there exists a group of shop-keepers (specifically, those who are also drivers) who are not engineers.
This directly supports the conclusion "Some shop-keepers are not engineers". This conclusion logically follows from Statements 2 and 3.
Summary of Conclusions:
- Conclusion 1: Some men are drivers. (Does NOT follow)
- Conclusion 2: No shop-keepers are engineer. (Does NOT follow)
- Conclusion 3: Some shop-keepers are not engineers. (Follows)
Based on the analysis, only Conclusion 3 logically follows from the given statements.
| Statement Type | Description | Example | Representation |
|---|---|---|---|
| A (Universal Affirmative) | All A are B | All cats are mammals | A <span>⊂</span> B |
| E (Universal Negative) | No A is B | No fish are birds | A <span>∩</span> B = <span>∅</span> |
| I (Particular Affirmative) | Some A are B | Some students are athletes | A <span>∩</span> B <span>≠</span> <span>∅</span> |
| O (Particular Negative) | Some A are not B | Some food is not healthy | A <span>∩</span> B<span><sup>c</sup></span> <span>≠</span> <span>∅</span> |
Revision Table: Key Inference Rules
| Statements | Valid Conclusion (if any) |
|---|---|
| A + A | A (e.g., All M are P, All S are M → All S are P) |
| A + E | E (e.g., All M are P, No S is M → No S is P) or E (e.g., No M is P, All S are M → No S is P) |
| A + I | I (e.g., All M are P, Some S are M → Some S are P) |
| E + A | E (e.g., No P is M, All S are M → No S is P) or O (e.g., No M is P, All M are S → Some S are not P) |
| E + I | O (e.g., No M is P, Some S are M → Some S are not P) or O (e.g., No P is M, Some M are S → Some S are not P) |
| I + A | I (e.g., Some M are P, All M are S → Some S are P) or I (e.g., Some P are M, All M are S → Some S are P) |
| I + E | O (e.g., Some M are P, No M is S → Some P are not S) or O (e.g., Some P are M, No M is S → Some P are not S) |
| O + A | O (e.g., Some M are not P, All M are S → Some S are not P) |
| Note: Two particular premises (I+I, I+O, O+I, O+O), two negative premises (E+E, E+O, O+E, O+O) yield no valid conclusion in classical syllogisms. | |
Additional Information on Logic Reasoning
This type of problem is based on deductive reasoning, specifically categorical syllogisms or statement-conclusion logic. The key is to deduce information strictly from the given statements, even if they contradict real-world knowledge.
- Categorical Statements: These are statements that relate two categories or classes. The statements here ("No man is engineer", "No engineer is driver", "Some drivers are shop-keepers") are categorical statements. They involve quantifiers like "No" (universal) and "Some" (particular).
- Middle Term: In syllogisms, a middle term connects the two premises. In this case, 'engineer' connects the first two statements, and 'driver' connects the second and third statements. Valid conclusions are often drawn through this connecting term.
- Validity vs. Truth: In logic problems, we are concerned with validity, not truth. A valid argument is one where if the premises are true, the conclusion *must* be true. We assume the statements are true for the sake of logical deduction.
- Negative Premises: Two negative premises (like E+E) generally yield no valid conclusion in classical syllogisms regarding the two extreme terms. Our first two statements are E+E ("No man is engineer," "No engineer is driver"), which is why we couldn't connect 'man' and 'driver'.
- Particular and Universal: A conclusion can only be universal ('All' or 'No') if both relevant premises are universal. If one premise is particular ('Some' or 'Some...not'), the valid conclusion (if any) must be particular. Our statements include 'Some drivers are shop-keepers', which is why a particular conclusion about shop-keepers (like Conclusion 3) is possible, while a universal conclusion (like Conclusion 2) is unlikely unless strongly supported otherwise.
Similar Questions
- All flowers are plants. Some plants are flowering plants. Which conclusion is logically valid?
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 f act s, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some carpenters are singers.
All singers are doctors.
Conclusions:
I. No doctor is a carpenter.
II. Some doctors are singers.
III. Some carpenters are doctors.
Three statements are given, followed by three conclusions numbered I, II and III. Assuming the statement s 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 machines are coolers.
All coolers are robots.
Some microwaves are coolers.
Conclusions:
I. Some coolers are machines.
II. Some robots are machines.
III. No robot is a microwave.
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:
1. All teachers are students.
2. All principal are teachers.
3. Some principals are doctors.
Conclusions:
I. Some students are teachers.
II. No student is a doctor.
III. Some students are principals.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.
III. No mango is an apple.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:
1. No bed is a chair.
2. All tables are beds.
3. No cupboard is a bed.
Conclusions:
I. No table is a chair.
II. No cupboard is a table.
III. Some beds are tables.
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. 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.
lII. No state is a zone.
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. 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.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is ture, 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 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.
Read the given statements and conclusions carefully. Assuming that the information given in the statement 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 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.
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:
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.
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 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.
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 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.
