Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. You have to decide which conclusion's logically follow/s from the given statements. Statements: Some books are horses. All horses are animals. Some animals are oceans. Conclusion (I): Some horses are oceans. Conclusion (II): Some animals are books.
Only conclusion (II) is true.
Logical Reasoning: Analyzing Statements and Conclusions
This question requires us to analyze the relationship between different categories based on the given statements and determine which of the provided conclusions logically follow.
Understanding the Given Statements
We are given the following statements:
- Some books are horses. (This indicates an overlap between the category of Books and the category of Horses.)
- All horses are animals. (This means that the category of Horses is completely contained within the category of Animals. Every member of the set of Horses is also a member of the set of Animals.)
- Some animals are oceans. (This indicates an overlap between the category of Animals and the category of Oceans.)
We must accept these statements as true, even if they contradict common knowledge.
Understanding the Conclusions to Evaluate
We need to check the validity of the following conclusions based on the statements:
- Conclusion (I): Some horses are oceans.
- Conclusion (II): Some animals are books.
Detailed Analysis of Conclusions
Let's evaluate each conclusion separately based on the provided statements.
Analyzing Conclusion (I): Some horses are oceans.
The statements establish connections between Books and Horses, Horses and Animals, and Animals and Oceans.
- We know all Horses are Animals.
- We know some Animals are Oceans.
The statement "Some animals are oceans" tells us there is an overlap between the set of Animals and the set of Oceans. However, this overlap could be with any part of the Animals. It could be with the Animals that are also Horses, or it could be with the Animals that are NOT Horses. The statements do not provide enough information to confirm that the overlap specifically includes the Horses.
Consider the possible relationships:
| Statement | Implication for Conclusion (I) |
|---|---|
| All horses are animals. | Horses are a subset of Animals. |
| Some animals are oceans. | Overlap exists between Animals and Oceans. |
Because the overlap between Animals and Oceans is only partial ("Some"), and Horses are just one part of the Animals, we cannot definitively conclude that any Horses are included in this overlap. Therefore, Conclusion (I) does not logically follow from the given statements.
Analyzing Conclusion (II): Some animals are books.
Let's look at the relevant statements:
- Some books are horses.
- All horses are animals.
The statement "Some books are horses" means there is at least one item that is both a Book and a Horse. Let's call this item 'X'. So, X is a Book and X is a Horse.
The statement "All horses are animals" means that every single Horse is also an Animal. Since X is a Horse, according to this statement, X must also be an Animal.
So, we have found an item X that is both a Book and an Animal (because it is a Book, it is a Horse, and because it is a Horse, it is an Animal). If there is at least one item that is both an Animal and a Book, then it logically follows that "Some animals are books" (specifically, item X and anything else like it).
Consider the connections:
| Relationship | Based on Statement |
|---|---|
| Some Books are Horses | Directly stated |
| All Horses are Animals | Directly stated |
| Some Books are also Animals | Inferred: Since some Books are Horses, and all Horses are Animals, those specific Books must also be Animals. |
| Some Animals are Books | Rephrased: If some Books are Animals, then it means there's an overlap, implying some Animals are Books. |
Therefore, Conclusion (II) logically follows from the given statements.
Summary of Conclusions
- Conclusion (I): Some horses are oceans. — Does not follow.
- Conclusion (II): Some animals are books. — Follows.
Based on this analysis, only Conclusion (II) is true.
Revision Table: Statements and Conclusions Logic
Understanding the types of statements in logical reasoning is crucial:
| Statement Type | Example | Description |
|---|---|---|
| All A are B | All cats are animals. | Set A is completely inside Set B. |
| Some A are B | Some cats are black. | There is at least one member common to both Set A and Set B. Could be some, many, or even all. |
| No A are B | No cats are dogs. | Set A and Set B have no members in common. |
| Some A are not B | Some cats are not black. | There is at least one member in Set A that is not in Set B. |
In our problem, we used "Some A are B" and "All A are B". The key inference from "Some A are B" and "All B are C" is "Some A are C". This aligns with our finding for Conclusion (II) where A=Books, B=Horses, C=Animals. "Some Books are Horses" and "All Horses are Animals" leads to "Some Books are Animals," which is equivalent to "Some Animals are Books."
Additional Information: Syllogism Basics
This type of question is based on Syllogism, a form of logical reasoning where a conclusion is drawn from two or more statements (premises). In syllogism problems:
- The statements are the premises that must be accepted as true.
- Conclusions are tested for whether they logically follow from these premises.
- Venn diagrams are often used as a visual aid to represent the relationships between categories described in the statements and check the validity of conclusions.
- If a conclusion is true in every possible diagram or scenario that satisfies the statements, then it is considered logically to follow. If there is even one possible scenario where the conclusion is false while the statements are true, then the conclusion does not follow.
For Conclusion (I), "Some horses are oceans," we could draw a diagram where the "Animals" circle and "Oceans" circle overlap, but this overlap area is entirely outside the smaller "Horses" circle (which is inside "Animals"). Since this is a possibility consistent with the statements, Conclusion (I) is not necessarily true and therefore does not logically follow.
For Conclusion (II), "Some animals are books," any valid diagram representing "Some Books are Horses" and "All Horses are Animals" will inevitably show an overlap between "Animals" and "Books" (specifically, the area representing "Horses" which overlaps with "Books" and is inside "Animals"). This overlap area confirms "Some Animals are Books".
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 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.
In the question below are given three statements followed by two conclusions. You have to take each of the given statements to be true. Read the conclusions and then decide which of the conclusions can be logically derived.
Statements:
Some schools are colleges.
No college is university.
All universities are hospitals.
Conclusions:
I. Some schools are universities.
II. At least some hospitals are colleges.
