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 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 cards are postcards.
Some cards are envelopes.
All envelopes are copies.
Conclusions:
I. Some copies are envelopes.
II. Some postcards are copies.
III. Some cards are copies.
Consider the given statement(s) to be true and decide which of the given conclusions/assumptions can definitely be drawn from the given statement.
Statement 1: All elephants are men.
Statement 2: All men are socks.
Conclusion I: Some socks are elephants.
Conclusion II: All elephants are socks.In the question, a word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the question are represented by two classes of alphabets in two matrices given below. The columns and rows of Matrix 1 are numbered from 0 to 4 and that of Matrix II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, e.g., 'A' can be represented by 04, 12, etc., and 'U' can be represented by 59, 66, etc. Similarly, you have to identify the set for the word 'ROOT'.
MATRIX I
0 1 2 3 4 0 B C D E A 1 D E A B C 2 C D E A B 3 A B C D E 4 E A B C D MATRIX II
5 6 7 8 9 5 R O N T U 6 T U R O N 7 O N T U R 8 U R O N T 9 N T U R O Consider the given statement/s to be true and decide which of the given conclusions/assumptions can definitely be drawn from the given statement.
Statements: 1. All fish are tortoise.
2. No tortoise is a crocodile.
Conclusion: 1. No crocodile is a fish.
II. No fish is a crocodile.
Consider the given statements to be true and decide which of the given conclusions/assumptions can definitely be drawn from the given statement.
Statements: 1. All books are novels.
2. Some novels are poems.
Conclusions: I. Some books are poems.
II. Some poems are novels.Consider the statement to be true and decide which of the conclusions logically follow:
Statement:
All dogs are animals.
All animals are living beings.
Conclusion
I:Dog is not an animal.
II. Dog is an animal.In the question, a word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the matrices are represented by two classes of alphabets as in two matrices given below. The columns and rows of Matrix I are numbered from 0 to 4 and that of Matrix II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, e.g., 'A' can be represented by 01, 13, etc., and 'S' can be represented by 55, 66, etc. Similarly, you have to identify the set for the word 'BOTH'.
MATRIX I
0 1 2 3 4 0 F A N O I 1 I O F A N 2 A N O I F 3 O F I N A 4 N I A F O MATRIX II
5 6 7 8 9 5 S E H B T 6 H S E T B 7 B T S E H 8 E H T B S 9 T S E H B Consider the given statement/s to be true and decide which of the given conclusions/assumptions can definitely be drawn from the given statement.
Statement I: All astronomers are scientists.
Statement II: Some scientists are shopkeepers.
Conclusion I: All astronomers are shopkeepers.
Conclusion II: All astronomers are scientists.
Conclusion III: Some shopkeepers are astronomers.
Conclusion IV: All scientists are astronomers.A word is represented by only one set of numbers as given in any one of the options. The sets of numbers are formed using two matrices below. The rows and columns of Matrix I are numbered 0 to 4 and Matrix II are numbered 5 to 9. A letter is represented by its row and column numbers. For example, ‘G’ can be coded as 12 or 21, and ‘L’ as 76 or 67.
Find the correct code for the word ‘LIFE’.
Consider the given statement/s to be true and decide which of the given conclusions/assumptions can definitely be drawn from the given statement:
Statements: Some cars are caves.
Conclusion: I. Some cars are not buses
II. Some caves are buses
III. No cave is a bus
IV. Some caves are cars
Important Questions from Syllogism
The statements below are followed by conclusions labeled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All twenty are thirty.
All thirty are forty.
All forty are sixty.
All sixty are seventy.
Conclusions:
I. Some forty are thirty.
II. Some seventy are sixty.
III. No thirty is twenty.The statements below are followed by two conclusions labelled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All Strong are animals.
Some animals are Tigers.
All Tigers are Sharp.
Conclusions:
I. Some Strong are Sharp.
II. No Strong is Sharp.The statements below are followed by conclusions labelled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some women are weak.
Some weaks are female.
All female are iron.
All iron are gold.Conclusions:
I. Some weaks are iron.
II. Some gold are weaks.
III. Some women are female.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some teaspoons are glasses.
All teddies are teaspoons.
Conclusions:
I. Some teddies are glasses.
II. Some glasses are teddies.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally Established facts, decide which conclusion(s) logically and definitely follow(s) from the Information, Given in the Statements.
Statements:
All bangles are rings.
Some rings are toys.
Some toys are dolls.
Conclusions:
I. Some rings are bangles.
II. Some dolls are rings.
