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.
Only conclusions I and II follow
Understanding Logical Deduction: Statements and Conclusions
This question asks us to determine which conclusions logically follow from the given statements. This is a common type of problem in logical reasoning and syllogism, where we analyze the relationship between different categories based on universal or particular statements.
Let's look at the given statements and conclusions:
Statements:
- All teachers are engineers.
- All clerks are teachers.
Conclusions:
- Some engineers are clerks.
- Some teachers are clerks.
- Some clerks are not engineers.
To solve this type of problem, we can use Venn diagrams. Each statement can be represented as a relationship between sets (categories).
Analyzing Statements with Venn Diagrams
Let's represent the categories: Clerks (C), Teachers (T), and Engineers (E).
- Statement 1: All teachers are engineers. This means the set of Teachers (T) is completely contained within the set of Engineers (E).
- Statement 2: All clerks are teachers. This means the set of Clerks (C) is completely contained within the set of Teachers (T).
Now, let's combine these two statements. If all clerks are teachers, and all teachers are engineers, then it logically follows that all clerks must also be engineers. The Venn diagram would show the set of Clerks inside the set of Teachers, and the set of Teachers inside the set of Engineers. So, the order of containment is C < T < E.
Evaluating Conclusions based on Logical Deduction
Let's evaluate each conclusion based on the combined understanding from the statements:
- Conclusion I: Some engineers are clerks.
Based on our combined understanding, all clerks are engineers. If there are any clerks, they are also engineers. The statement "Some engineers are clerks" means there is at least one engineer who is also a clerk. Since all clerks are engineers, and assuming there are clerks, this conclusion is true. If there are clerks, they fall into the category of engineers, thus 'some' engineers are indeed clerks. This conclusion logically follows.
- Conclusion II: Some teachers are clerks.
Based on Statement 2, "All clerks are teachers". This means the set of clerks is inside the set of teachers. The statement "Some teachers are clerks" means there is at least one teacher who is also a clerk. Since all clerks are teachers, and assuming there are clerks, this conclusion is true. Clerks are a subset of teachers, so there are teachers who are clerks. This conclusion logically follows.
- Conclusion III: Some clerks are not engineers.
Based on the combined statements, "All clerks are engineers". This means there are no clerks who are not engineers. The statement "Some clerks are not engineers" contradicts the deduction that all clerks are engineers. Therefore, this conclusion does not follow.
Summary of Conclusions
After analyzing each conclusion, we found that:
- Conclusion I follows.
- Conclusion II follows.
- Conclusion III does not follow.
Therefore, only conclusions I and II logically follow from the given statements.
| Statement/Conclusion | Relationship | Logical Follows? |
|---|---|---|
| Statement 1: All T are E | T is a subset of E | Given |
| Statement 2: All C are T | C is a subset of T | Given |
| Combined: All C are E | C is a subset of T, T is a subset of E, so C is a subset of E | Deduced |
| Conclusion I: Some E are C | Since all C are E, if C exists, then some E are C. | Yes |
| Conclusion II: Some T are C | Since all C are T, if C exists, then some T are C. | Yes |
| Conclusion III: Some C are not E | Contradicts "All C are E". | No |
This analysis shows that only conclusions I and II are valid.
Revision Table: Syllogism Rules
| Statement Type (Categorical Proposition) | Form | Example | Description |
|---|---|---|---|
| A (Universal Affirmative) | All S are P | All dogs are mammals. | The entire subject class is included in the predicate class. |
| E (Universal Negative) | No S are P | No dogs are cats. | The entire subject class is excluded from the predicate class. |
| I (Particular Affirmative) | Some S are P | Some dogs are brown. | At least one member of the subject class is included in the predicate class. |
| O (Particular Negative) | Some S are not P | Some dogs are not brown. | At least one member of the subject class is excluded from the predicate class. |
In our problem, "All teachers are engineers" and "All clerks are teachers" are 'A' type propositions. The conclusions "Some engineers are clerks" and "Some teachers are clerks" are 'I' type propositions. "Some clerks are not engineers" is an 'O' type proposition.
Additional Information: Solving Syllogisms
Syllogisms are a form of logical argument where a conclusion is drawn from two premises (statements). The key is to understand the relationships between the categories (or terms) involved. The middle term connects the two premises (in this case, 'Teachers' is the middle term as it appears in both statements).
Venn diagrams are a visual tool that helps represent the sets and their overlaps or containment. Drawing the diagrams for the statements and then checking if the conclusions hold true in the diagram is a reliable method. Alternatively, one can learn syllogistic rules or use methods like the square of opposition and conversion rules, but Venn diagrams are often the most intuitive for beginners.
Remember that in logic, we assume the statements are true, even if they don't match real-world facts. We only follow what the statements logically imply.
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.
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.
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.
