Three statements are given followed by three conclusions numbered I, II and Ill. Question ID: 264330143712 Status : Answered Chosen Option : 1 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 males are boys. Some teachers are boys. All students are teachers. Conclusions: I. Some boys are males. II. Some teachers are students. Ill. All males are students.
Only conclusions I and II follow
Solving the Syllogism: Statements and Conclusions
Let's analyze the given statements and conclusions to determine which conclusions logically follow. We can represent these statements using Venn diagrams or by analyzing the relationships directly.
Analysis of Statements
We have three statements:
- Statement 1: All males are boys. ($\text{Males} \subset \text{Boys}$)
- Statement 2: Some teachers are boys. (Intersection of $\text{Teachers}$ and $\text{Boys}$ is non-empty)
- Statement 3: All students are teachers. ($\text{Students} \subset \text{Teachers}$)
From these statements, we can deduce some relationships:
- Since All males are boys, the set of Males is a subset of the set of Boys.
- There is an overlap between the set of Teachers and the set of Boys.
- The set of Students is entirely contained within the set of Teachers.
Let's visualize the relationships based on the statements:
- Set of Males is inside the set of Boys.
- Set of Students is inside the set of Teachers.
- Set of Teachers overlaps with the set of Boys.
Note that the overlap between Teachers and Boys could include individuals who are Students (since Students are Teachers) or individuals who are Teachers but not Students. The overlap could also include individuals who are Males (since Males are Boys) or individuals who are Boys but not Males.
Evaluating the Conclusions
Now let's examine each conclusion based on the statements:
Conclusion I: Some boys are males.
Statement 1 says "All males are boys". If all members of set A are members of set B, then it logically follows that some members of set B must be members of set A (specifically, the members of set A). For example, if all apples are fruits, then some fruits are apples. Thus, if All males are boys, then Some boys are males.
Conclusion I logically follows from Statement 1.
Conclusion II: Some teachers are students.
Statement 3 says "All students are teachers". Similar to Conclusion I, if all members of set A are members of set B, then it logically follows that some members of set B must be members of set A. If All students are teachers, then Some teachers are students.
Conclusion II logically follows from Statement 3.
Conclusion III: All males are students.
We know All males are boys. We know Some teachers are boys. We know All students are teachers. We need to determine if this forces all males to be students.
- Males are inside the circle of Boys.
- Students are inside the circle of Teachers.
- Teachers and Boys circles overlap.
Consider a male. By Statement 1, this male is a boy. By Statement 2, some teachers are boys, meaning the intersection of Teachers and Boys is not empty. However, this doesn't tell us if the specific boy (who is a male) is a teacher. By Statement 3, all students are teachers. Even if a male boy is a teacher, he is not necessarily a student unless he falls into the specific subset of teachers who are students.
There is no statement or combination of statements that guarantees that every male is also a student. It is possible to construct a scenario where a male is a boy, this boy is also a teacher, but this teacher is not one of the teachers who is a student. It is also possible a male is a boy, but this boy is not among the "some boys" who are teachers.
Therefore, the conclusion "All males are students" does not logically follow from the given statements.
Conclusion III does not logically follow.
Summary of Conclusions
- Conclusion I: Some boys are males. (Follows)
- Conclusion II: Some teachers are students. (Follows)
- Conclusion III: All males are students. (Does not follow)
Based on our analysis, only Conclusion I and Conclusion II logically follow from the given statements.
| Conclusion | Logically Follows? | Reasoning |
|---|---|---|
| I. Some boys are males. | Yes | Derived from "All males are boys". If All A are B, Some B are A. |
| II. Some teachers are students. | Yes | Derived from "All students are teachers". If All A are B, Some B are A. |
| III. All males are students. | No | No direct connection established between All Males and All Students from the statements. |
Revision Table: Syllogism Concepts
| Concept | Explanation | Example |
|---|---|---|
| Universal Affirmative (All A are B) | Every member of class A is a member of class B. | All dogs are mammals. |
| Particular Affirmative (Some A are B) | At least one member of class A is a member of class B. | Some students are athletes. |
| Converse of "All A are B" | "Some B are A". This is a valid inference. | Converse of "All dogs are mammals" is "Some mammals are dogs". |
| Converse of "Some A are B" | "Some B are A". This is a valid inference. | Converse of "Some students are athletes" is "Some athletes are students". |
Additional Information: Rules of Inference in Syllogisms
Understanding basic rules of inference helps in solving syllogism problems. Some key points:
- From a universal statement ("All A are B"), a particular statement ("Some A are B") can be directly inferred. For example, if All humans are mortal, then Some humans are mortal.
- The converse of a universal affirmative statement ("All A are B") is a particular affirmative statement ("Some B are A"). This is a valid inference.
- The converse of a particular affirmative statement ("Some A are B") is also a particular affirmative statement ("Some B are A"). This is a valid inference.
- It is generally not possible to infer a universal conclusion from two particular premises.
- It is not possible to infer anything definite about the relationship between two sets if the middle term connecting them is qualified by "some" in both relevant statements. In this case, 'boys' connects 'males' (via All males are boys) and 'teachers' (via Some teachers are boys). We cannot reliably connect males and teachers universally or even particularly through 'boys' based on these statements alone.
Applying these principles confirms our evaluation of the conclusions.
Similar Questions
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. All rugs are blankets.
2. All blankets are pillows.
3. Some blankets are frames.
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I. All pillows are rugs.
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All whites are pinks.
All pinks are oranges.
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I. No M is R.
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III. Some R are A.
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.
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All c are f.
No f is t.
All p are c.
Conclusions:
I. Some t are c.
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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 bottles are towels.
No towel is a pillow.
All bottles are coats.
Conclusions:
I. Some coats are towels.
II. No coat is a towel.
III. Some bottles are pillows.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 Tim are Jack.
No Jack is Ben.
Some Ben is Ruth.
Conclusions:
I. No Ruth is Jack.
II. Some Ben are Jack.
III. No Ben is Tim.
In this question, 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 follows/follow from the statements.
Statements:
Some roses are yellow.
Some yellow are buses.
All buses are green.
Conclusions:
I. All yellow are roses.
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III. All yellow are green.
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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.
