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 plates are bowls. No bowl is a glass. Some glasses are vessels. Conclusions: I. Some glasses are plates. II. Some bowls are plates. III. Some vessels are bowls.
Only conclusion II follows.
Understanding the Syllogism Problem
This problem requires us to analyze a set of statements and determine which of the given conclusions logically follow from them. We must assume the statements are true, even if they contradict real-world knowledge.
Analyzing the Statements
We are given three statements:
- Statement 1: All plates are bowls.
- Statement 2: No bowl is a glass.
- Statement 3: Some glasses are vessels.
Let's represent these statements mentally or using a visual aid like Venn diagrams to understand the relationships between 'plates', 'bowls', 'glasses', and 'vessels'.
Evaluating the Conclusions
Now, let's examine each conclusion based on the given statements:
Conclusion I: Some glasses are plates.
From Statement 1, we know that all plates are contained within the set of bowls. From Statement 2, we know that the set of bowls and the set of glasses are completely separate (they have no overlap). Since plates are inside bowls, and bowls have no overlap with glasses, it means plates also have no overlap with glasses. Therefore, no plate is a glass, and consequently, no glass is a plate.
Thus, Conclusion I does not logically follow from the statements.
Conclusion II: Some bowls are plates.
Statement 1 says "All plates are bowls." If every single plate is also a bowl, this implies that the set of plates is a subset of the set of bowls. If there are plates, then there must be at least some bowls that are also plates (specifically, all the bowls that are plates). This is a direct logical deduction from the universal affirmative statement "All A are B" implies "Some B are A".
Thus, Conclusion II logically follows from the statements.
Conclusion III: Some vessels are bowls.
Statement 3 tells us that there is some overlap between the set of glasses and the set of vessels. Statement 2 tells us that there is no overlap between the set of bowls and the set of glasses. We know some vessels are glasses, and we know no glasses are bowls. The vessels that are glasses cannot be bowls. The statements do not give us any information about the vessels that are *not* glasses. We cannot establish a direct or indirect link that guarantees an overlap between the set of vessels and the set of bowls based only on the given information. The portion of vessels that overlaps with glasses is disjoint from bowls.
Thus, Conclusion III does not logically follow from the statements.
Summary of Conclusions
- Conclusion I: Some glasses are plates. (Does not follow)
- Conclusion II: Some bowls are plates. (Follows)
- Conclusion III: Some vessels are bowls. (Does not follow)
Based on our analysis, only Conclusion II logically follows from the given statements.
Final Answer Derivation
We determined that only Conclusion II is logically valid based on the provided statements.
| Statement/Conclusion | Validity | Reasoning |
|---|---|---|
| Statement 1: All plates are bowls. | Assumed True | Given |
| Statement 2: No bowl is a glass. | Assumed True | Given |
| Statement 3: Some glasses are vessels. | Assumed True | Given |
| Conclusion I: Some glasses are plates. | Does not follow | Plates are within bowls; bowls & glasses are disjoint. Hence, plates & glasses are disjoint. |
| Conclusion II: Some bowls are plates. | Follows | If all plates are bowls, then some bowls must be plates. (Conversion of A proposition) |
| Conclusion III: Some vessels are bowls. | Does not follow | Some glasses are vessels; no bowls are glasses. No direct link established between vessels and bowls. |
Revision Table: Key Syllogism Rules
| Statement Type | Form | Conversion | Example |
|---|---|---|---|
| Universal Affirmative (A) | All S are P | Some P are S (Valid) | All cats are mammals $\implies$ Some mammals are cats. |
| Universal Negative (E) | No S are P | No P are S (Valid) | No dogs are cats $\implies$ No cats are dogs. |
| Particular Affirmative (I) | Some S are P | Some P are S (Valid) | Some students are tall $\implies$ Some tall people are students. |
| Particular Negative (O) | Some S are not P | Not Valid (Cannot convert) | Some animals are not dogs $\implies$ Some dogs are not animals (Invalid). |
Additional Information: Understanding Logical Deduction
Logical deduction is the process of reasoning from one or more general statements (premises or statements) to reach a logically certain conclusion. In syllogisms, if the premises are true, and the reasoning is valid, the conclusion must also be true. When solving syllogism problems, it's crucial to rely only on the information provided in the statements, ignoring any outside knowledge.
Venn diagrams are a helpful tool to visualize the relationships described by the statements. Each set (like 'plates', 'bowls') is represented by a circle, and the overlap or separation of circles represents the relationship between the sets.
- "All A are B": Circle A is completely inside Circle B.
- "No A are B": Circle A and Circle B are separate.
- "Some A are B": Circles A and B overlap, indicating at least one common element.
By combining the diagrams for the statements, you can check if the conclusion holds true in all possible valid arrangements.
Similar Questions
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 pencils are colours.
All colours are paints.
Some paints are drawings.
Conclusions:
I. Some pencils are drawings.
II. Some paints are colours.
III. Some colours are pencils
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:
Some teachers are scientists.
All scientists are doctors.
All doctors are engineers.
Conclusions:
I. Some doctors are teachers.
II. Some engineers are teachers.
III. Some doctors are scientists.
Three statements are given followed by three conclusions numbered I, Il and lII. 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 fruits are wines.
Some wines are juices.
All juices are alcohols.
Conclusions:
I. Some alcohols are juices.
Il. Some wines are alcohols.
III. Some wines are fruits.
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 rugs are blankets.
2. All blankets are pillows.
3. Some blankets are frames.
Conclusions:
I. All pillows are rugs.
II. Some pillows are rugs.
III. All rugs are frames
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 polygons are angles.
All angles are diagonals.
All cones are cubes.
All cubes are decagons.
No diagonal is a cube.
Conclusions:
I. Some diagonals are polygons.
II. All diagonals are decagons.
III. No polygon is a cone.
IV. Some cubes are angles.
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 T are G.
II. All G are H.
Conclusions:
I. All T are H.
II. No G is T.
III. All H are G.
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 reds are pinks.
All whites are pinks.
All pinks are oranges.
Conclusions:
I. All whites are oranges.
II. All oranges are reds.
III. Some oranges are whites.
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 R are M.
II. All L are M.
Conclusions:
I. Some M are not R.
II. Some L are R.
III. Some M are L.
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 M are A.
II. No A is R.
Conclusion:
I. No M is R.
II. Some A are M.
III. Some R are A.
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 c are f.
No f is t.
All p are c.
Conclusions:
I. Some t are c.
II. No p is t.
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.
