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
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 curtains are pillows.
No pillow is a bedsheet.
Some curtains are bedsheets.
Conclusions:
I. No curtain is a bedsheet.
II. No pillow is a curtain.
III. Some bedsheets are curtains.
IV. Some pillows are curtains.
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 dates are cashews.
All cashews are raisins.
Some raisins are almonds.
Conclusions:
I. All almonds being dates is a possibility.
II. All dates are raisins.
III. No cashew is an almond.
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 vehicles are helicopters.
All helicopters are cars.
Conclusions:
I. All vehicles are cars.
II. Some vehicles are cars.
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 plants are flowers.
Some flowers are fruits.
All flowers are gardens.
Conclusions:
I. Some gardens are plants.
II. Some fruits are gardens.
III. Some gardens are flowers.
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.
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 classrooms are schools.
No school is a park.
All houses are parks.
Conclusions:
I. No house is a classroom.
II. No park is a classroom.
III. No school is a house.
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 fans are hammers.
All hammers are fishes.
Conclusions:
I. No fans are fishes.
II. Some fans are fishes.
Read the given statements and conclusions carefully. Assuming that the information given in the statement 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 fans are coolers.
All coolers are equipment.
Some equipment are mobiles.
Conclusions:
I. Some equipments are fans.
II. Some mobiles are fans.
III. No equipment is fan and cooler both
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 inkpots are kettles.
All utensils are candies.
No kettle is utensil.
Conclusions:
1. Some inkpots are candies.
2. Some kettles are inkpots.
3. Some candies are inkpots.
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 holders are hangers.
All hangers are hammers.
Some hammers are axes.
Conclusions:
I. Some axes are hangers.
II. Some hammers are holders.
III. Some hangers are holders.
Important Questions from Conventional 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:
1. Some flowers are chemicals.
2. Some chemicals are herbs.
Conclusions:
I. No flower is a herb.
II. Some flowers are herbs.
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 students are teachers.
All teachers are professors.
Conclusions:
1. All students are professors.
2. All professors are students.
3. No teacher is a professor.
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 dentists are surgeons.
II. All the surgeons are doctors.
Conclusions:
I. Some dentists are doctors.
II. No surgeons are dentists.
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 at variance with generally established facts. decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
1) Some angers are griefs.
2) Some griefs are loves.
Conclusion:
I. Some griefs are angers.
II. Some loves are griefsThe 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 cows are deer.
Some deer are fishes.
Conclusion:
I. Some cows are fishes.
II. Some fishes are cows.
