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: 1) Some trousers are pants. 2) All pants are jeans. 3) All jeans are coats. Conclusions: I. All pants are coats. II. At least some trousers are jeans
Both conclusions I and II follow
Understanding Syllogism Statements and Conclusions
This question asks us to analyze given statements and determine which of the provided conclusions logically follow. This type of problem is based on logical reasoning, specifically syllogisms.
Analyzing the Given Statements
We are given the following statements:
| Statement Number | Statement |
|---|---|
| 1 | Some trousers are pants. |
| 2 | All pants are jeans. |
| 3 | All jeans are coats. |
We must assume these statements are true, regardless of real-world facts.
Analyzing the Given Conclusions
We need to evaluate the truthfulness of the following conclusions based on the statements:
| Conclusion Number | Conclusion |
|---|---|
| I | All pants are coats. |
| II | At least some trousers are jeans. |
Step-by-Step Logical Analysis
Let's evaluate each conclusion one by one using the information from the statements.
Analyzing Conclusion I: All pants are coats.
To check if "All pants are coats" logically follows, we look at the statements involving 'pants' and 'coats'.
- Statement 2 says: All pants are jeans. (P → J)
- Statement 3 says: All jeans are coats. (J → C)
If every single pant is a jean (Statement 2), and every single jean is a coat (Statement 3), then it logically follows that every single pant must also be a coat. This is a standard rule of logic known as the transitive property or chain rule for universal affirmative statements.
Symbolically, if \( A \rightarrow B \) and \( B \rightarrow C \), then \( A \rightarrow C \).
Applying this rule here: If All Pants are Jeans, and All Jeans are Coats, then All Pants are Coats. Therefore, Conclusion I logically follows from statements 2 and 3.
Analyzing Conclusion II: At least some trousers are jeans.
To check if "At least some trousers are jeans" logically follows, we look at the statements involving 'trousers' and 'jeans'.
- Statement 1 says: Some trousers are pants.
- Statement 2 says: All pants are jeans.
Statement 1 tells us there is at least one trouser that is also a pant. Statement 2 tells us that every single pant is also a jean. If there is at least one trouser that belongs to the group of pants, and every member of the group of pants also belongs to the group of jeans, then that specific trouser (or trousers) must also belong to the group of jeans.
Think of it like this: If some students are in the Chess Club, and all students in the Chess Club are also in the Math Club, then it must be true that some students (those in the Chess Club) are also in the Math Club.
Applying this logic: Since Some trousers are pants, and All pants are jeans, it logically follows that At least some trousers are jeans. Therefore, Conclusion II logically follows from statements 1 and 2.
Summary of Findings
Based on our analysis:
- Conclusion I ("All pants are coats") follows from Statements 2 and 3.
- Conclusion II ("At least some trousers are jeans") follows from Statements 1 and 2.
Since both conclusions logically follow from the given statements, the correct option is the one that states both conclusions I and II follow.
Revision Table: Key Concepts in Syllogism
| Concept | Description | Example from Statements |
|---|---|---|
| Universal Affirmative (All) | Every member of one category is a member of another category. Represented as "All A are B". | All pants are jeans. (Statement 2) |
| Particular Affirmative (Some) | At least one member of one category is also a member of another category. Represented as "Some A are B". | Some trousers are pants. (Statement 1) |
| Transitive Property / Chain Rule | If All A are B and All B are C, then All A are C. | Statements 2 & 3 lead to Conclusion I. |
| Syllogism with 'Some' and 'All' | If Some A are B and All B are C, then Some A are C. | Statements 1 & 2 lead to Conclusion II. |
Additional Information: Types of Logical Relationships
Syllogism problems test your understanding of different types of logical relationships between categories. The common types of statements include:
- Universal Affirmative (A): All S are P (e.g., All dogs are mammals)
- Universal Negative (E): No S are P (e.g., No fish are birds)
- Particular Affirmative (I): Some S are P (e.g., Some students are athletes)
- Particular Negative (O): Some S are not P (e.g., Some fruits are not apples)
In this problem, we dealt with Universal Affirmative ('All') and Particular Affirmative ('Some') statements and derived conclusions based on how these categories overlap or are included within each other according to the statements.
Remember, in logic problems like this, you must strictly adhere to the information given in the statements and not bring in outside knowledge.
Similar Questions
Two 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 teachers are engineers.
All clerks are teachers.
Conclusions:
I. Some engineers are clerks.
II. Some teachers are clerks.
III. Some clerks are not engineers.
Two statements are given followed by two conclusions numbered I and II. 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 keys are locks.
All locks are handles.
Conclusions:
I. Some locks are keys.
II. Some handles are keys.
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 switches are fans.
No heater is a fan.
Some wires are heaters.
Conclusions:
I. Some wires are fans.
II. No switch is a heater.
III. No wire is a switch.
Three statements are given followed by two conclusions numbered I and II. 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 H are G.
All V are H.
Some V are I.
Conclusions:
I. At least some G are I.
II. All I being H is a possibility.
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 beds are chairs.
Some chairs are tables.
All tables are cupboards.
Conclusions :
I. Some tables are beds.
II. Some cupboards are chairs.
III. Some cupboards are beds.
Read the given statement(s) 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 statement(s).
Statements :
Some ceilings are beds.
No bed is an apple.
All dogs are beds.
Conclusions :
I. Some ceilings being dogs is a possibility.
II. No dog is an apple.
III. All beds are dogs.
IV. No ceiling is an apple.
Two statements are given followed by two conclusions numbered I and II. 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 keys are locks.
All locks are handles.
Conclusions:
I. All locks are keys.
II. All handles are keys.
Two statements are given followed by two conclusions numbered I and II. 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 windows are doors.
No window is a cupboard.
Conclusions:
I. No cupboard is a door.
II. Some doors are definitely not cupboard.
Three Statements are given followed by Four conclusions numbered I, II, III and IV. 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 copies are pillows.
Some pillows are laptops.
Some laptops are pens.
Conclusions:
I. Some copies are laptops.
II. Some pillows are pens.
III. Some pens are laptops.
IV. Some pens are pillows.
Three statements are given followed by two conclusions numbered I and II. 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 crow is a monkey.
All monkeys are turtles.
No turtle is a snail.
Conclusions :
I. Some snails being crows is a possibility.
II. No turtle is a crow.
Important Questions from Conventional Syllogism
In this question, three statements followed by two conclusions numbered I and II have been given. You have to take the given statements to be true even if they seem to be at variance from the commonly facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statements: Some flats are apartments.
No apartment is a hall.
Some halls are rooms.
Conclusions: I. At least some rooms are flats.
II. No apartment is a room.
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:
I. Some blue are red.
II. Some green are red.
Conclusions:
I. No blue is green.
II. No red is green.
Given below are two statements, Consider these statements to be true even if they seem factuality absurd, Read the conclusions and then decide which of the given conclusions logically follow(s) from the given statements?
Statements :
1. All vases are flowers.
2. No flowers is a plant.
Conclusions :
1. No vases is a plant.
2. Some plant are vases
In the question two statements are given, followed by three conclusions, I, II and III. You have to consider the statements to be true even if it seems to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements.
Statement 1 : Some cars are scooters.
Statement 2 : All scooters are buses.
Conclusion I : Some scooters are cars.
Conclusion II : Some buses are cars.
Conclusion III : All cars are buses.
Read the given statements and conclusions carefully. Assuming that the information in the statement is true even if they appear to be at variance with commonly known facts, choose the conclusion that logically follows from the statement beyond reasonable doubt.
Statement:-
1. Some dogs are cats.
2. All cats are birds.
Conclusion:-
1. Some dogs are birds.
2. No cat is dog.
