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
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 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.
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 blankets are quilts.
Some quilts are bedsheets.
Conclusions:
I. All quilts are blankets.
II. All blankets are bedsheets.
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.
