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.
Only conclusion II follows
Understanding Syllogisms: Vehicles, Helicopters, and Cars
This question requires us to analyze logical statements and determine which conclusions necessarily follow from them. This type of problem is known as a syllogism, a form of logical reasoning where a conclusion is derived from two or more statements (premises).
Analyzing the Syllogism Statements
We are given two statements:
- Statement 1: Some vehicles are helicopters.
- Statement 2: All helicopters are cars.
Let's break down what each statement means in terms of sets or categories:
- Statement 1 tells us there is at least one vehicle that is also a helicopter. It doesn't say *all* vehicles are helicopters, nor does it say *no* vehicles are helicopters (unless explicitly stated otherwise, which it isn't here). It establishes an overlap between the set of 'vehicles' and the set of 'helicopters'.
- Statement 2 tells us that the entire set of 'helicopters' is contained within the set of 'cars'. If something is a helicopter, it *must* also be a car.
Combining the Statements Logically
Now, let's combine the information from both statements. We know that some vehicles are part of the 'helicopters' group (Statement 1). We also know that the entire 'helicopters' group is part of the 'cars' group (Statement 2).
If we consider the specific vehicles mentioned in Statement 1 (the ones that are helicopters), by Statement 2, these same vehicles must also be cars because they belong to the set of helicopters, and all helicopters are cars.
This establishes a link: Some Vehicles $\rightarrow$ Helicopters $\rightarrow$ Cars. The vehicles that are helicopters are necessarily cars.
Evaluating the Syllogism Conclusions
Let's examine each conclusion based on our combined understanding of the statements.
Conclusion I: All vehicles are cars analysis
This conclusion claims that every single vehicle is also a car. However, the statements do not provide enough information to support this claim. Statement 1 only talks about *some* vehicles being helicopters (and thus cars). It says nothing about the other vehicles (those that are *not* helicopters). We cannot conclude that those other vehicles are also cars based solely on the given statements.
For this conclusion to be true, we would need a statement like "All vehicles are helicopters" or "All vehicles are cars" or "All things that are not helicopters are also cars" (which would be implied if "All vehicles are cars" were true). We don't have any such information.
Therefore, Conclusion I does not logically follow from the statements.
Conclusion II: Some vehicles are cars analysis
This conclusion claims that there is at least one vehicle that is also a car. From Statement 1, we know that some vehicles are helicopters. Let's call this group of vehicles 'X'. So, 'X' is a subset of Vehicles, and 'X' is also a subset of Helicopters. From Statement 2, we know that all helicopters are cars. Since 'X' is a subset of Helicopters, and all Helicopters are Cars, 'X' must also be a subset of Cars.
So, the vehicles in group 'X' (which we know exist because Statement 1 says "Some vehicles are helicopters") are also cars. This means that some vehicles are indeed cars.
Therefore, Conclusion II logically follows from the statements.
Summary of Logical Deductions
Based on our analysis:
- Conclusion I ("All vehicles are cars") does not follow because the statements only provide information about a portion of vehicles.
- Conclusion II ("Some vehicles are cars") follows because the vehicles that are helicopters (as per Statement 1) must also be cars (as per Statement 2).
Thus, only Conclusion II follows from the given statements.
Syllogism Concepts Revision Table
| Quantifier | Meaning in Syllogisms | Example |
|---|---|---|
| All | Every member of the first category is also a member of the second. (Complete inclusion) | All A are B (A is a subset of B) |
| Some | At least one member of the first category is also a member of the second. Could be 'some but not all', 'all', or 'exactly one'. (Partial overlap) | Some A are B (Overlap between A and B) |
| No | Not a single member of the first category is a member of the second. (Complete separation) | No A are B (A and B are disjoint) |
Additional Information on Syllogism Reasoning
Syllogisms are a fundamental part of deductive reasoning. They help us understand how conclusions can be drawn based on given premises. When solving syllogism problems, it's important to:
- Assume the statements are true, even if they contradict common knowledge.
- Analyze the relationship between the categories mentioned in the statements.
- Visualize the relationships, perhaps using Venn diagrams, which can make it easier to see overlaps and inclusions.
- Strictly follow the logic implied by the statements and avoid bringing in outside information or assumptions.
- Pay close attention to quantifiers like "All", "Some", and "No", as they define the extent of the relationship between categories.
In the case of "Some A are B" and "All B are C", the logical deduction "Some A are C" is always valid. This is a classic pattern in syllogistic reasoning.
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.
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.
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 black is white.
Some white is grey.
Conclusions:
I. Some grey is black.
II. Some white is black.
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.
