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 follows from the statements. Statements: Some bowls are cups. All cups are glasses. Some glasses are plates. All plates are utensils. Conclusions: I. All bowls cannot be utensils. II. All glasses cannot be utensils
Neither conclusion I nor II follows
Analyzing Statements and Conclusions on Bowls, Cups, Glasses, Plates, and Utensils
The problem requires us to evaluate two conclusions based on a set of given statements. We must assume the statements are true and determine which conclusions logically follow from them.
Understanding the Statements
Let's break down the given statements:
- Some bowls are cups. (This indicates an overlap between the set of bowls and the set of cups.)
- All cups are glasses. (This means the entire set of cups is contained within the set of glasses.)
- Some glasses are plates. (This indicates an overlap between the set of glasses and the set of plates.)
- All plates are utensils. (This means the entire set of plates is contained within the set of utensils.)
Evaluating Conclusion I: All bowls cannot be utensils.
This conclusion claims it's impossible for all bowls to be utensils. Let's see if we can construct a scenario (a possible Venn diagram representation) where all bowls are utensils, without contradicting any of the statements.
- From statement 1 & 2: Some bowls are cups, and all cups are glasses. This implies that some bowls are glasses.
- From statement 3 & 4: Some glasses are plates, and all plates are utensils. This implies that some glasses are utensils.
Now consider if all bowls can be utensils. The statements only guarantee that some bowls are glasses (because they are cups). What about the other bowls (if any)? Or even the bowls that are glasses? The statements do not restrict bowls from being plates or utensils directly. It is possible to draw a diagram where:
- Some bowls are cups (and thus glasses).
- The part of bowls that are glasses overlaps with plates (which are utensils).
- The remaining bowls (those not cups) are also within the set of utensils (perhaps overlapping with plates or just being utensils directly).
For instance, imagine if the set of 'bowls' was entirely contained within the set of 'utensils'. This would not contradict any statement: 'Some bowls are cups' could still be true (that specific 'some' portion of bowls is also cups and thus utensils), 'All cups are glasses' would be true, 'Some glasses are plates' would be true, and 'All plates are utensils' would be true. Since it is possible for all bowls to be utensils, the conclusion "All bowls cannot be utensils" does not logically follow.
Evaluating Conclusion II: All glasses cannot be utensils.
This conclusion claims it's impossible for all glasses to be utensils. Let's see if we can construct a scenario where all glasses are utensils, without contradicting any of the statements.
- From statement 3 & 4: Some glasses are plates, and all plates are utensils. This directly implies that some glasses are utensils.
Can all glasses be utensils? The statements only guarantee that some glasses are utensils (specifically, the ones that are plates). What about the rest of the glasses? The statements do not restrict glasses from being utensils. It is possible to draw a diagram where:
- The entire set of glasses is contained within the set of utensils.
- The 'some glasses' that are plates (and thus utensils) exist within this larger set of glasses.
Since statement 3 says "Some glasses are plates" and statement 4 says "All plates are utensils", we know that the set of plates is a subset of glasses AND a subset of utensils. This guarantees an overlap between glasses and utensils. However, this does not preclude the possibility that the entire set of glasses is also a subset of utensils. Since it is possible for all glasses to be utensils, the conclusion "All glasses cannot be utensils" does not logically follow.
Conclusion Summary
Based on our analysis:
- Conclusion I ("All bowls cannot be utensils") does not follow because it is possible for all bowls to be utensils.
- Conclusion II ("All glasses cannot be utensils") does not follow because it is possible for all glasses to be utensils.
Therefore, neither conclusion logically follows from the given statements.
| Statement | Relationship |
|---|---|
| Some bowls are cups. | Bowls ∩ Cups ≠ ∅ |
| All cups are glasses. | Cups ⊂ Glasses |
| Some glasses are plates. | Glasses ∩ Plates ≠ ∅ |
| All plates are utensils. | Plates ⊂ Utensils |
Result
Neither conclusion I nor conclusion II follows from the given statements.
Revision Table: Syllogism Basics
| Term | Explanation |
|---|---|
| Statement (Premise) | A proposition assumed to be true for the purpose of an argument. |
| Conclusion | A proposition that is claimed to follow logically from the statements. |
| Syllogism | A form of deductive reasoning where a conclusion is drawn from two or more given premises. |
| Follows Logically | Means the conclusion must be true if the statements are true, in all possible scenarios consistent with the statements. |
| Does Not Follow | Means there is at least one possible scenario consistent with the statements where the conclusion is false. |
Additional Information: Types of Statements in Syllogism
Statements in syllogism problems typically fall into one of four categories:
- Universal Affirmative (A): All S are P. (e.g., All cups are glasses)
- Universal Negative (E): No S are P. (e.g., No cups are plates)
- Particular Affirmative (I): Some S are P. (e.g., Some bowls are cups)
- Particular Negative (O): Some S are not P. (e.g., Some glasses are not plates)
Understanding these types helps in visually representing the relationships using Venn diagrams or analyzing them using rules of logic. "Cannot be" in a conclusion often implies a particular negative statement, or checking for the possibility of the opposite (a universal affirmative or particular affirmative).
Similar Questions
- Read the following statement carefully and identify the conclusion that follows.
Statement:
All poets are writers. Some writers are critics. No critic is a fool.
Conclusions:
I. Some poets are critics.
II. Some writers are not fools. - Statements: All dancers are artists. No artist is lazy.
Conclusions: I. No dancer is lazy. II. Some lazy are dancers. - Read the following statement carefully and identify the conclusion that follows.
Statement:
All oranges are fruits. No fruit is a vegetable. All vegetables are green.
Conclusions:
I. No orange is green.
II. No orange is a vegetable. - Read the following statement carefully and identify the conclusion that follows.
Statement:
All kids are students. Some students are athletes. No athlete is a scholar.
Conclusions:
I. Some kids may be athletes.
II. No kid is a scholar. - Statements: Some keys are locks. Some locks are doors.
Conclusions: I. Some keys are doors. II. All locks being keys is a possibility. - Read the following statement carefully and identify the conclusion that follows.
Statement:
All musicians are artists. Some artists are dancers. No dancer is blind.
Conclusions:
I. Some artists are not blind.
II. All blind are not dancers. Statements: Some pens are papers. All papers are books. Conclusions: I. Some pens are books. II. All books are pens.
Read the following statement carefully and identify the conclusion that follows.
Statement:
All birds are animals. Some animals are tigers. No tiger is a bird.
Conclusions:
I. Some tigers are birds.
II. Some animals are not birds.
- Statements: All dogs are cats. Some cats are rats. Conclusions: I. Some rats are dogs. II. All dogs are rats.
Read the following statement carefully and identify the conclusion that follows.
Statement:
All pens are blue things. Some blue things are plastic. No plastic is recyclable.
Conclusions:
I. Some pens are plastic.
II. Some blue things are not recyclable.
Important Questions from Syllogism
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:
Some students are players.
All players are male.
Conclusions:
I. All males are players.
II. Some males are students.
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:
No creative is an employer.
All experts are creative.
All workers are experts.
Conclusions:
I. No employer is an expert.
II. No worker is an employer.
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:
Some actors are choreographers.
All choreographers are producers.
Not a single producer is a director.
Conclusions:
I. Some actors are directors.
II. Not a single actor is a director.
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 flowers are tulips.
2. No tulips are whites.
Conclusions :
I. All tulips are flowers.
II. Some tulips are whites.
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 rats are dogs.
Some rats are hens.
Conclusions:
I. Some rats are dogs.
II. Some hens are rats.
