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 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.
