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 follows from the statements.
Statements:
All lemons are plums.
All plums are dates.
Some dates are mangoes.
Conclusions:
I. Some lemons are mangoes.
II. Some mangoes are plums.
III. All lemons are dates.
IV. Some mangoes are dates.
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.
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 spices are medicines.
All medicines are chemicals.
No chemical is cheap.
Conclusions:
I. Some medicines are cheap.
II. Some chemicals are spices.
III. No medicine is cheap.
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 oranges are apples.
Some oranges are bananas.
All bananas are fruits.
Conclusions:
I. Some fruits are apples.
II. Some apples are bananas.
III. Some oranges are fruits.
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 Z are X.
II. Some W are Z.
Conclusions:
I. Some X are not W.
II. Some X are not Z.
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 mobiles are flat.
All flats are TVs.
Some TVs are plastic.
Conclusions:
I. Some mobiles are TVs.
II. Some flats are plastic.
III. All plastic are TVs.
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 cup is a plate.
All cups are utensils.
Some bottles are cups.
Conclusions:
I. Some utensils are not plates.
II. Some bottles are not plates.
III. No bottle is a plate.
Three statements are followed by three conclusions numbered I, II and III. You have to consider these statements to be true, even if they seem to be at variance with commonly known facts. Decide which of the given conclusions logically follow/s from the given statements.
Statements:
Some watches are projectors.
All projectors are lamps.
Some heaters are watches.
Conclusions:
(I) Some heaters are projectors.
(II) Some lamps are heaters.
(III) All watches are lamps
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. No A is B.
II. No C is B.
Conclusion:
I. Some C are not A.
II. Some A are B.
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 benches are tables.
Some tables are chairs.
Some chairs are pencils.
Conclusions:
I. Some benches are chairs.
II. Some tables are pencils.
III. Some pencils are chairs.
IV. Some pencils are tables.
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.
