In this question three statements are given followed by three conclusions I, II and III. You have to consider the three 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(s) logically follow(s) from the given statements. Statements: All photocopiers are computers. Some computers are laptops. No laptop is a mobile. Conclusions: (I) No computer is a mobile. (II) Some computers are photocopiers. (III) All mobiles are photocopiers.
Only conclusion II follows.
Understanding Syllogism Statements and Conclusions
This question asks us to analyze the logical relationship between three statements and three potential conclusions. In syllogism, we assume the given statements are absolutely true, even if they contradict common knowledge, and then determine which conclusions logically follow from these statements.
Analyzing the Given Statements
Let's break down the statements provided:
- Statement 1: All photocopiers are computers.
- Statement 2: Some computers are laptops.
- Statement 3: No laptop is a mobile.
We can represent these relationships using set notation or by visualizing them with Venn diagrams. Let's use a combination of description and potential diagram interpretation.
From Statement 1, the set of 'photocopiers' is entirely contained within the set of 'computers'.
From Statement 2, there is an overlap between the set of 'computers' and the set of 'laptops'. This overlap means there's at least one computer that is also a laptop.
From Statement 3, the set of 'laptops' and the set of 'mobiles' have no elements in common. They are mutually exclusive sets.
Evaluating the Conclusions
Now let's examine each conclusion based on the statements.
Conclusion I: No computer is a mobile.
Statement 2 tells us "Some computers are laptops". Statement 3 tells us "No laptop is a mobile". This means the computers that are laptops cannot be mobiles. However, Statement 2 also implies that there might be computers that are NOT laptops. The statements give us no information about whether these computers (that are not laptops) can or cannot be mobiles. Therefore, we cannot definitively conclude that no computer is a mobile. It is possible that some computers that are not laptops could be mobiles. Conclusion I does not logically follow.
Conclusion II: Some computers are photocopiers.
Statement 1 says "All photocopiers are computers". This is a universal positive statement. If all photocopiers belong to the category of computers, it necessarily implies that the category of computers contains at least some elements that are photocopiers (assuming there is at least one photocopier). The relationship "All A are B" logically implies "Some B are A". Therefore, if all photocopiers are computers, it logically follows that some computers are photocopiers. Conclusion II logically follows from Statement 1.
Conclusion III: All mobiles are photocopiers.
Statement 3 says "No laptop is a mobile". Statements 1 and 2 relate photocopiers and laptops to computers. There is no direct link established between mobiles and photocopiers. We know mobiles are not laptops. We also know photocopiers are a subset of computers. There is no information allowing us to conclude that all mobiles must be photocopiers. This conclusion does not logically follow from the given statements.
Summary of Conclusions
| Conclusion | Logically Follows? | Reasoning |
|---|---|---|
| I: No computer is a mobile. | No | Some computers might not be laptops, and these could potentially be mobiles based on the given statements. |
| II: Some computers are photocopiers. | Yes | If all photocopiers are computers, then some computers must be photocopiers. |
| III: All mobiles are photocopiers. | No | No direct link between mobiles and photocopiers is established, and no combination of statements supports this. |
Based on our analysis, only Conclusion II logically follows from the given statements.
Revision Table: Syllogism Rules
| Statement Type | Relationship | Inference Example |
|---|---|---|
| All A are B | A ⊂ B | If All A are B, then Some B are A. |
| No A is B | A ∩ B = ∅ | If No A is B, then No B is A. |
| Some A are B | A ∩ B ≠ ∅ | If Some A are B, then Some B are A. |
| Some A are not B | A but not in B | Limited direct inferences. |
Additional Information on Syllogism Logic
Syllogism problems test your ability to follow logical deductions based *only* on the information provided in the statements. Common pitfalls include:
- Bringing in outside knowledge.
- Assuming "Some" means "Some but not all". In logic, "Some" means "at least one".
- Assuming relationships between categories that are not explicitly stated or can be inferred. For example, just because some A are B and some B are C, you cannot assume some A are C.
Practicing with Venn diagrams can help visualize the relationships and avoid making unwarranted assumptions. Remember to consider all possible scenarios allowed by the statements.
Similar Questions
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:
All teachers are engineers.
All clerks are teachers.
Conclusions:
I. Some engineers are clerks.
II. Some teachers are clerks.
III. Some clerks are not engineers.
Two 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 paintings are calligraphies.
All sketching are calligraphies .
Conclusions:
I. At least some calligraphies are paintings.
II. No sketching is a painting.
Two 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:
Some vehicles are helicopters.
All helicopters are cars.
Conclusions:
I. All vehicles are cars.
II. Some vehicles are cars.
Given below are two statements and two conclusions. Take the statements to be true even if they are at variance with commonly known facts, and decide whether the conclusion(s) follow(s) the given statements.
Statements:
All eyes are noses.
Some noses are lips.
Conclusions:
I. Some noses are eyes.
II. All lips are noses.
Two statements are given followed by conclusions numbered 1 and 2. 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. Some mammals are animals.
2. All animals are birds.
Conclusions:
1. All birds are animals.
2. Some mammals are birds.
Two 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 keys are locks.
All locks are handles.
Conclusions:
I. Some locks are keys.
II. Some handles are keys.
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:
All switches are fans.
No heater is a fan.
Some wires are heaters.
Conclusions:
I. Some wires are fans.
II. No switch is a heater.
III. No wire is a switch.
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 H are G.
All V are H.
Some V are I.
Conclusions:
I. At least some G are I.
II. All I being H is a possibility.
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:
All apples are pineapples.
Some apples are mangoes.
No mango is a grape.
Conclusions:
I. Some pineapples are not grapes.
II. No pineapple is a grape.
III. Some apples are not grapes.
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:
No river is a sea.
Some rivers are lakes.
All rivers are ponds.
Conclusions:
I. Some lakes are seas.
II. Some ponds are seas.
III. Some lakes are ponds.
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.
