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: Some boys are brave. All boys are punctual. Conclusions: I. Some brave are boys. II. Some punctual are boys.
All conclusion follow
Understanding Syllogism Statements and Conclusions
The question presents two statements and three conclusions related to them. We need to determine which conclusions logically follow from the given statements, assuming the statements are true.
The statements are:
- Statement 1: Some boys are brave.
- Statement 2: All boys are punctual.
The conclusions are:
- Conclusion I: Some brave are boys.
- Conclusion II: Some punctual are boys.
- Conclusion III: Some brave are punctual.
Analyzing Each Conclusion Based on Statements
Let's analyze each conclusion to see if it can be logically derived from the statements.
Analysis of Conclusion I: Some brave are boys.
Statement 1 says, "Some boys are brave." This is a particular affirmative statement. The conclusion "Some brave are boys" is the simple converse of this statement. In standard logic, the converse of "Some A are B" is "Some B are A," and this conversion is valid. If there is an overlap between the group of 'boys' and the group of 'brave' people (meaning some individuals belong to both groups), then it naturally follows that some members of the 'brave' group are also members of the 'boys' group.
Therefore, Conclusion I logically follows from Statement 1.
Analysis of Conclusion II: Some punctual are boys.
Statement 2 says, "All boys are punctual." This is a universal affirmative statement. The conclusion "Some punctual are boys" relates the terms 'boys' and 'punctual'. If all individuals in the 'boys' group are also in the 'punctual' group, it means the 'boys' group is entirely contained within the 'punctual' group. If the set of all boys is a subset of the set of punctual people, then some members of the larger 'punctual' set must be the members of the 'boys' set. Specifically, all the boys are punctual, which implies that at least some (in fact, all) of the boys are punctual, and therefore, some punctual individuals are boys. This conclusion follows from the rules of immediate inference (specifically, sub-alternation followed by conversion of an A statement).
Therefore, Conclusion II logically follows from Statement 2.
Analysis of Conclusion III: Some brave are punctual.
This conclusion connects the terms 'brave' and 'punctual' using the middle term 'boys'.
- Statement 1: Some boys are brave.
- Statement 2: All boys are punctual.
From Statement 1, we know there is at least one boy who is brave. Let's call this boy 'X'. So, X is a boy and X is brave.
From Statement 2, we know that all boys are punctual. Since X is a boy, it follows that X is also punctual.
So, we have an individual X who is both brave and punctual. This means there is at least one individual who is both brave and punctual. This is precisely what the conclusion "Some brave are punctual" states.
This conclusion follows from combining Statement 1 and Statement 2. It's a standard deduction in syllogism where a particular statement (Some B are Br) and a universal affirmative statement (All B are P) lead to a particular affirmative conclusion (Some Br are P), provided the middle term is distributed appropriately (which 'boys' is in the 'All boys are punctual' statement).
Therefore, Conclusion III logically follows from the statements.
Summary of Conclusions
Based on our analysis:
- Conclusion I (Some brave are boys) follows from Statement 1.
- Conclusion II (Some punctual are boys) follows from Statement 2.
- Conclusion III (Some brave are punctual) follows from Statement 1 and Statement 2 combined.
Since all three conclusions logically follow from the given statements, the correct answer is that all conclusions follow.
Revision Table: Syllogism Rules Applied
| Conclusion | Statements Involved | Syllogism Principle / Inference | Follows? |
|---|---|---|---|
| I. Some brave are boys. | Statement 1: Some boys are brave. | Conversion of 'Some A are B' to 'Some B are A' | Yes |
| II. Some punctual are boys. | Statement 2: All boys are punctual. | Inference from 'All A are B' implies 'Some B are A' | Yes |
| III. Some brave are punctual. | Statement 1: Some boys are brave. Statement 2: All boys are punctual. |
Combination of I-A statements (Some B are Br, All B are P → Some Br are P) | Yes |
Additional Information: Basic Syllogism Concepts
Syllogism is a form of logical reasoning where a conclusion is drawn from two given or assumed propositions (statements). These propositions share a common or middle term, which is absent in the conclusion.
Types of Categorical Propositions:
- A: Universal Affirmative (All S are P)
- E: Universal Negative (No S are P)
- I: Particular Affirmative (Some S are P)
- O: Particular Negative (Some S are not P)
Immediate Inference: Drawing a conclusion from a single statement, e.g., Conversion (swapping subject and predicate). Conversion of 'Some A are B' is 'Some B are A', which is valid.
Mediate Inference (Syllogism): Drawing a conclusion from two statements. For a valid syllogism, certain rules must be followed regarding the distribution of terms and the quality/quantity of statements.
In this problem:
- Statement 1: Some boys (Middle Term) are brave (Major Term/Minor Term). (I type)
- Statement 2: All boys (Middle Term) are punctual (Major Term/Minor Term). (A type)
- Conclusion III: Some brave (Major Term/Minor Term) are punctual (Major Term/Minor Term). (I type)
The structure of the statements (I and A) and the conclusion (I), with 'boys' as the middle term, follows a valid syllogistic form (specifically, IAI in the third figure or reducible to first figure). The other conclusions are valid immediate inferences from the individual statements.
Important Questions from 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:
Some students are players.
All players are male.
Conclusions:
I. All males are players.
II. Some males are students.
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:
No creative is an employer.
All experts are creative.
All workers are experts.
Conclusions:
I. No employer is an expert.
II. No worker is an employer.
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 actors are choreographers.
All choreographers are producers.
Not a single producer is a director.
Conclusions:
I. Some actors are directors.
II. Not a single actor is a director.
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 flowers are tulips.
2. No tulips are whites.
Conclusions :
I. All tulips are flowers.
II. Some tulips are whites.
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 rats are dogs.
Some rats are hens.
Conclusions:
I. Some rats are dogs.
II. Some hens are rats.
