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.
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.
