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.
Only conclusion II follows
Understanding Syllogism Statements and Conclusions
This question requires us to analyze given statements and determine which conclusions logically follow from them. This type of problem falls under the category of logical reasoning, specifically syllogisms. We must assume the statements are true, even if they contradict general knowledge.
Analyzing the Given Statements
We have two statements:
- Some fans are hammers.
- All hammers are fishes.
These statements describe relationships between three categories: fans, hammers, and fishes.
Visualizing the Relationships (Venn Diagrams)
We can use Venn diagrams to represent these relationships visually. Let's denote the set of fans as F, the set of hammers as H, and the set of fishes as Fi.
- Statement 1: "Some fans are hammers." This means there is at least one element that belongs to both the set of fans (F) and the set of hammers (H). The intersection of sets F and H is not empty.
- Statement 2: "All hammers are fishes." This means every element in the set of hammers (H) is also in the set of fishes (Fi). The set H is a subset of the set Fi.
Now, let's combine these two statements. Since there are some fans that are hammers (from statement 1), and all hammers are fishes (from statement 2), it logically follows that those 'some fans' who are also 'hammers' must also be 'fishes'.
This establishes an intersection between the set of fans (F) and the set of fishes (Fi). Specifically, the elements that are in the intersection of F and H are guaranteed to be in Fi because H is a subset of Fi.
Evaluating the Conclusions
Let's examine each conclusion based on our analysis of the statements:
Conclusion I: No fans are fishes.
Based on our combined understanding of the statements, we found that there is an intersection between fans and hammers, and since all hammers are fishes, this intersection also lies within fishes. Therefore, there are some fans that are fishes. Conclusion I, stating "No fans are fishes," directly contradicts this finding. Thus, conclusion I does not logically follow from the given statements.
Conclusion II: Some fans are fishes.
As explained above, because some fans are hammers (Statement 1) and all hammers are fishes (Statement 2), the group of 'some fans' who are also 'hammers' must necessarily be included within the group of 'fishes'. This confirms that there are some fans that are also fishes. Therefore, conclusion II logically follows from the given statements.
Summary of Conclusions
| Conclusion | Statement | Logically Follows? |
|---|---|---|
| I. No fans are fishes. | States there is no overlap between fans and fishes. | No, contradicts findings. |
| II. Some fans are fishes. | States there is at least some overlap between fans and fishes. | Yes, supported by combined statements. |
Based on the logical derivation from the statements, only conclusion II follows.
Revision Table: Syllogism Basics
| Term | Explanation | Example |
|---|---|---|
| Statement | A proposition assumed to be true for the purpose of the argument. | All A are B. |
| Conclusion | A proposition derived from the statements. | Therefore, Some A are C. |
| Syllogism | A form of deductive reasoning where a conclusion is derived from two or more statements. | Statement 1: All birds are animals. Statement 2: All animals are living beings. Conclusion: All birds are living beings. |
| Venn Diagram | A visual representation used to show relationships between sets. Useful for analyzing syllogisms. | Overlapping circles representing categories. |
Additional Information: Types of Statements in Syllogisms
Syllogistic statements typically fall into four types:
- Universal Affirmative (A): All S are P. (e.g., All dogs are mammals)
- Universal Negative (E): No S are P. (e.g., No cats are dogs)
- Particular Affirmative (I): Some S are P. (e.g., Some students are tall)
- Particular Negative (O): Some S are not P. (e.g., Some fruits are not sweet)
In our problem:
- "Some fans are hammers" is a Particular Affirmative (I) statement.
- "All hammers are fishes" is a Universal Affirmative (A) statement.
The combination of an I statement and an A statement can often lead to an I conclusion, as seen in this case ("Some fans are fishes").
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.
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 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
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.
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.
In the question below are given three statements followed by two conclusions. You have to take each of the given statements to be true. Read the conclusions and then decide which of the conclusions can be logically derived.
Statements:
Some schools are colleges.
No college is university.
All universities are hospitals.
Conclusions:
I. Some schools are universities.
II. At least some hospitals are colleges.
