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 scooters are planes. Conclusions: I. Some plants are scooters.
Some planes are dogs.
Some dogs are plants.
II. No plane is scooter.
Neither Conclusion I nor II follows
Analyzing the Syllogism Statements and Conclusions
This question asks us to evaluate two conclusions based on three given statements. We need to determine which conclusion(s) logically and definitely follow from the statements, assuming the statements are true.
Understanding the Statements
The statements provide relationships between different categories:
- Some scooters are planes.
- Some planes are dogs.
- Some dogs are plants.
These are all 'Some' statements, indicating a partial overlap between the categories mentioned.
Evaluating Conclusion I: Some plants are scooters.
Conclusion I tries to establish a relationship between 'plants' and 'scooters'. Let's look at the chain of relationships given in the statements:
Scooters <--Some--> Planes <--Some--> Dogs <--Some--> Plants
The statements show a connection from scooters to planes, planes to dogs, and dogs to plants, but each connection is only partial ('Some'). When you have a chain of 'Some' relationships like this, you cannot definitively conclude a 'Some' relationship between the first and the last category (scooters and plants).
For example, it's possible that the "some" scooters that are planes are different from the "some" planes that are dogs, and these "some" dogs are different from the "some" dogs that are plants, resulting in no overlap between scooters and plants. While they *might* overlap, the statements do not guarantee it. Therefore, Conclusion I does not logically and definitely follow.
Evaluating Conclusion II: No plane is scooter.
Conclusion II states that there is absolutely no overlap between 'planes' and 'scooters'. Let's compare this to the first statement:
Statement 1: Some scooters are planes.
This statement explicitly tells us that there is an overlap between scooters and planes; specifically, at least some scooters are planes (which also means at least some planes are scooters, as 'Some A are B' implies 'Some B are A'). Conclusion II, "No plane is scooter," directly contradicts this first statement.
Since the statements are assumed to be true, and Statement 1 is true, Conclusion II, which says the opposite, cannot logically follow. Therefore, Conclusion II does not logically and definitely follow.
Final Decision
Based on our evaluation, neither Conclusion I nor Conclusion II logically and definitely follows from the given statements.
| Statement/Conclusion | Relationship | Evaluation | Follows Logically? |
|---|---|---|---|
| Statement 1 | Some scooters are planes | Given as true | N/A |
| Statement 2 | Some planes are dogs | Given as true | N/A |
| Statement 3 | Some dogs are plants | Given as true | N/A |
| Conclusion I | Some plants are scooters | Chain of 'Some' statements; no definite link between non-adjacent terms. | No |
| Conclusion II | No plane is scooter | Directly contradicts Statement 1 ("Some scooters are planes"). | No |
Revision Table: Syllogism Logic
| Statement Type | Conclusion Type | Validity | Notes |
|---|---|---|---|
| Some A are B, Some B are C | Some A are C | Invalid | Cannot conclude 'Some' between A and C from two 'Some' premises. |
| All A are B, All B are C | All A are C | Valid | Transitivity holds for 'All' statements. |
| All A are B, Some B are C | Some A are C | Invalid | No definite link between A and C. |
| Some A are B | No A is B | Invalid | Contradicts the premise. |
| No A is B | Some A are B | Invalid | Contradicts the premise. |
Additional Information: Syllogism Rules
Syllogism questions test your ability to derive logical conclusions strictly from given statements, ignoring outside knowledge. Key points include:
- Only what is stated or can be definitively inferred from the statements is considered true.
- 'Some' means "at least one", and potentially includes "all". However, you cannot assume "all" from "some".
- Two 'Some' premises in a standard syllogism cannot yield a universal conclusion ('All' or 'No').
- Two 'Some' premises cannot yield a definite 'Some' conclusion about non-adjacent terms in a chain like the one presented.
- A conclusion that contradicts a given statement is never valid.
Using Venn diagrams can often help visualize the possible scenarios and check if a conclusion holds true in all of them.
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:
All dancers are talented.
Some girls are dancers.
Conclusions:
I. Some girls are talented.
II. All talented are girls.
III. All girls are talented.
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 directors are actors.
No actor is a producer.
All choreographers are directors.
Conclusions:
I. No choreographer is producer.
II. Some actors are choreographers.
III. No director is a producer.
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.
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 employees are tax-payers.
Some employees are farmers.
Some farmers are doctors.
Conclusions:
I. No farmer is a tax-payer.
II. Some farmers are tax-payers.
