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 bikes are cars. Some cars are trucks. All trucks are cycles. Conclusions: I. Some cars are cycles. II. Some cycles are trucks. III. Some bikes are trucks.
Only conclusions I and II follow.
Understanding Syllogism Questions
Syllogism is a form of logical reasoning where a conclusion is deduced from two or more propositions (statements). The key is to determine which conclusions logically follow from the given statements, assuming the statements are true.
Statements Provided
The given statements are:
- All bikes are cars.
- Some cars are trucks.
- All trucks are cycles.
Conclusions to Evaluate
We need to evaluate the following conclusions:
- Some cars are cycles.
- Some cycles are trucks.
- Some bikes are trucks.
Solving with Venn Diagrams
Venn diagrams are a helpful tool to visualize the relationships described in the statements. We can draw circles representing each category mentioned (Bikes, Cars, Trucks, Cycles) and show how they overlap or are contained within each other based on the statements.
Diagramming the Statements
Let's represent the statements:
- Statement 1: All bikes are cars. This implies the circle for 'Bikes' is drawn completely inside the circle for 'Cars'.
- Statement 2: Some cars are trucks. This indicates an overlap between the 'Cars' circle and the 'Trucks' circle. The overlapping area represents the cars that are also trucks.
- Statement 3: All trucks are cycles. This means the circle for 'Trucks' is drawn completely inside the circle for 'Cycles'. Since some cars are trucks (Statement 2), the area where cars and trucks overlap is also within the 'Cycles' circle.
Analyzing the Conclusions based on Diagrams
Let's check each conclusion:
Conclusion I: Some cars are cycles.
According to Statement 2, 'Some cars are trucks'. According to Statement 3, 'All trucks are cycles'. If some cars belong to the category of trucks, and the entire category of trucks is within the category of cycles, then those specific cars that are trucks must also be cycles. Therefore, there is definitely an overlap between 'Cars' and 'Cycles'. Conclusion I logically follows.
Conclusion II: Some cycles are trucks.
Statement 3 says 'All trucks are cycles'. This means that every single truck is also a cycle. If all trucks are cycles, then the set of trucks is a subset of the set of cycles. This directly implies that there are some cycles that are trucks (specifically, all the trucks). Conclusion II logically follows.
Conclusion III: Some bikes are trucks.
Statement 1 tells us 'All bikes are cars'. Statement 2 tells us 'Some cars are trucks'. We know bikes are inside the 'Cars' circle, and there is an overlap between 'Cars' and 'Trucks'. However, the overlap between 'Cars' and 'Trucks' might be in the portion of the 'Cars' circle that does not contain 'Bikes'. There is no information that guarantees an overlap between the 'Bikes' circle and the 'Trucks' circle. Therefore, we cannot conclude that some bikes are trucks. Conclusion III does not follow.
Results of Conclusion Analysis
Based on our analysis using Venn diagrams:
- Conclusion I follows.
- Conclusion II follows.
- Conclusion III does not follow.
Therefore, only conclusions I and II logically follow from the given statements.
Syllogism Statement Types Revision
| Type | Example | Relationship |
|---|---|---|
| Universal Affirmative (A) | All A are B | Every member of A is a member of B. |
| Universal Negative (E) | No A are B | No member of A is a member of B. |
| Particular Affirmative (I) | Some A are B | At least one member of A is a member of B. |
| Particular Negative (O) | Some A are not B | At least one member of A is not a member of B. |
Additional Information: Syllogism Basics
Syllogisms are a fundamental concept in deductive reasoning. They consist of premises (statements) that lead to a conclusion. A syllogism is considered valid if the conclusion logically follows from the premises, regardless of whether the premises or the conclusion are true in the real world.
Understanding the relationships implied by words like "All," "Some," and "No" is crucial. "Some" typically means "at least one." Syllogism problems are common in competitive exams to test logical aptitude.
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.
