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
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 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.
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:
All laptops are desktops.
All desktops are printers.
Some printers are monitors.
Conclusions:
I. Some laptops are monitors.
II. Some monitors are desktops.
III. All laptops are printers.
IV. Some monitors are printers.
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
Two statements are given followed by conclusions numbered 1 and 2. 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:
1. Some mammals are animals.
2. All animals are birds.
Conclusions:
1. All birds are animals.
2. Some mammals are birds.
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.
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.
In each question below are given three statements followed by two conclusions numbered I and II. You have to take the two/three given statements to be true even if they seem to be at variance from commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statement:
Some mobiles are laptops.
No laptop is computer.
All phones are computer.
Conclusion:
I. At least some mobiles are computer.
II. At least some phone are laptops.
