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.
Only conclusion III follows
Understanding Syllogism Statements and Conclusions
This question asks us to analyze a set of statements and determine which of the given conclusions logically follow. This type of problem is based on deductive reasoning, specifically syllogism.
Let's break down the given information:
Statements Provided
- Statement 1: No river is a sea.
- Statement 2: Some rivers are lakes.
- Statement 3: All rivers are ponds.
Conclusions to Evaluate
- Conclusion I: Some lakes are seas.
- Conclusion II: Some ponds are seas.
- Conclusion III: Some lakes are ponds.
We need to assume the statements are true, even if they contradict common knowledge, and see which conclusions *must* be true based solely on these statements.
Analyzing Each Conclusion Based on Statements
Evaluating Conclusion I: Some lakes are seas.
We know from Statement 2 that there is an overlap between rivers and lakes (\(\text{Some River} \cap \text{Lake}\)). From Statement 1, we know that rivers and seas have no overlap (\(\text{River} \cap \text{Sea} = \emptyset\)). The part of rivers that are lakes definitely cannot be seas, because no river can be a sea. However, the statements give us no direct information about the relationship between lakes and seas, or about the parts of lakes that are *not* rivers. Therefore, we cannot definitively conclude that some lakes are seas. This conclusion does not necessarily follow.
Evaluating Conclusion II: Some ponds are seas.
We know from Statement 3 that all rivers are ponds (\(\text{River} \subset \text{Pond}\)). This means that the set of rivers is entirely contained within the set of ponds. From Statement 1, we know that no river is a sea (\(\text{River} \cap \text{Sea} = \emptyset\)). Since all rivers are ponds, the part of ponds that consists of rivers cannot be seas. However, the statements provide no information about the parts of ponds that are *not* rivers, or any direct link between ponds and seas. Therefore, we cannot definitively conclude that some ponds are seas. This conclusion does not necessarily follow.
Evaluating Conclusion III: Some lakes are ponds.
Let's combine Statement 2 and Statement 3. Statement 2 says "Some rivers are lakes". This means there exists at least one entity that is both a river and a lake. Let's call this entity 'X'. So, X is a river AND X is a lake. Statement 3 says "All rivers are ponds". Since X is a river, and all rivers are ponds, X must also be a pond. Therefore, X is a lake AND X is a pond. This means there is at least one entity (X) that is both a lake and a pond. Thus, "Some lakes are ponds" logically follows from the statements.
Summary of Conclusion Analysis
- Conclusion I: Some lakes are seas - Does NOT follow.
- Conclusion II: Some ponds are seas - Does NOT follow.
- Conclusion III: Some lakes are ponds - Follows.
Based on our analysis, only Conclusion III logically follows from the given statements.
Revision Table: Syllogism Concepts
| Term | Meaning in Syllogism | Example Statement Type |
|---|---|---|
| Statements | Given propositions assumed to be true | All A are B, No A is B, Some A are B, Some A are not B |
| Conclusions | Propositions to be derived logically from statements | Follows necessarily or does not follow |
| Deductive Reasoning | Process of inferring conclusions from premises | Syllogism is a form of deductive reasoning |
| Validity | Whether the conclusion logically follows from the premises | A valid argument's conclusion is true if premises are true |
Additional Information: Syllogism Rules
Syllogism problems often involve analyzing the relationships between different categories. Here are some basic points to remember:
- If a statement says "All A are B" (\(\text{A} \subset \text{B}\)), it means every member of category A is also a member of category B.
- If a statement says "No A is B" (\(\text{A} \cap \text{B} = \emptyset\)), it means there is no overlap between category A and category B.
- If a statement says "Some A are B" (\(\text{A} \cap \text{B} \neq \emptyset\)), it means there is at least one member that belongs to both category A and category B. It does not mean *only* some, it means at least one, and possibly all.
- When combining statements, look for common terms that link the categories. In this problem, 'rivers' is the common term linking lakes, seas, and ponds.
- A conclusion follows only if it *must* be true in every possible scenario that satisfies the statements.
Visual aids like Venn diagrams can be very helpful in solving syllogism problems, allowing you to map out the relationships described by the statements and visually check if the conclusions hold true.
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.
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.
