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 boy is an engineer. No engineer is a driver. All girls are boys. Conclusions: I. All boys are drivers. II. No girl is an engineer.
Understanding Logical Statements and Conclusions
This question requires us to analyze given statements and determine which of the provided conclusions logically follow based solely on the information in the statements, even if that information contradicts general knowledge.
Analyzing the Statements
Let's break down the given statements:
- Statement 1: No boy is an engineer. This establishes a clear separation between the set of boys and the set of engineers. Their intersection is empty. We can represent this relationship as: $\text{Boys} \cap \text{Engineers} = \emptyset$.
- Statement 2: No engineer is a driver. Similarly, this states that the set of engineers and the set of drivers have no members in common. We can represent this as: $\text{Engineers} \cap \text{Drivers} = \emptyset$.
- Statement 3: All girls are boys. This is a statement of inclusion. The set of girls is a subset of the set of boys. Every member of the 'girls' set is also a member of the 'boys' set. We can represent this as: $\text{Girls} \subseteq \text{Boys}$.
Analyzing the Conclusions
Now let's evaluate each conclusion based on the statements:
Conclusion I: All boys are drivers.
Let's consider if this conclusion is supported by the statements:
- We know No boy is an engineer (Statement 1).
- We know No engineer is a driver (Statement 2).
These statements tell us about the relationship between boys and engineers, and between engineers and drivers. They do not provide any direct information about the relationship between boys and drivers. Just because engineers are separate from both boys and drivers does not mean that boys and drivers must overlap or that all boys must be drivers. It's possible for there to be boys who are not engineers and are also not drivers. Therefore, Conclusion I does not logically follow from the given statements.
Conclusion II: No girl is an engineer.
Let's consider if this conclusion is supported by the statements:
- We know All girls are boys (Statement 3). This means the set of girls is entirely contained within the set of boys.
- We know No boy is an engineer (Statement 1). This means the set of boys and the set of engineers have no common elements.
If all girls are members of the 'boys' set, and no member of the 'boys' set is an engineer, it logically follows that no member of the 'girls' set can be an engineer. If girls are boys, and no boys are engineers, then no girls are engineers. This conclusion is directly supported by combining Statement 3 and Statement 1.
Conclusion
Based on our analysis, only Conclusion II logically follows from the given statements.
| Statement/Conclusion | Relationship | Logical Status |
|---|---|---|
| Statement 1 | No boy is an engineer | Given (True) |
| Statement 2 | No engineer is a driver | Given (True) |
| Statement 3 | All girls are boys | Given (True) |
| Conclusion I | All boys are drivers | Does not follow |
| Conclusion II | No girl is an engineer | Logically follows |
Therefore, the correct answer is that only conclusion II follows.
Revision Table: Logical Reasoning Concepts
| Concept | Explanation |
|---|---|
| Statements | Propositions considered to be true for the purpose of the problem. |
| Conclusions | Inferences drawn from the statements. |
| Logically Follows | A conclusion follows if it must be true whenever the statements are true. |
| Syllogism | A form of deductive reasoning where a conclusion is derived from two or more premises (statements). |
Additional Information: Deductive Reasoning
This type of question tests deductive reasoning. Deductive reasoning involves starting with general statements (premises) and arriving at a specific conclusion. If the premises are true, then the conclusion reached through valid deduction must also be true. In these problems, we must strictly adhere to the information given in the statements and not use any outside knowledge or assumptions, even if the statements seem counter-intuitive. The relationships between categories (like boys, engineers, drivers, girls) are key to determining valid conclusions.
Important Questions from Syllogism
The statements below are followed by conclusions labeled I, II and III. 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:
All twenty are thirty.
All thirty are forty.
All forty are sixty.
All sixty are seventy.
Conclusions:
I. Some forty are thirty.
II. Some seventy are sixty.
III. No thirty is twenty.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 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:
All Strong are animals.
Some animals are Tigers.
All Tigers are Sharp.
Conclusions:
I. Some Strong are Sharp.
II. No Strong is Sharp.The statements below are followed by conclusions labelled I, II and III. 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 women are weak.
Some weaks are female.
All female are iron.
All iron are gold.Conclusions:
I. Some weaks are iron.
II. Some gold are weaks.
III. Some women are female.
The 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 teaspoons are glasses.
All teddies are teaspoons.
Conclusions:
I. Some teddies are glasses.
II. Some glasses are teddies.
The 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:
All bangles are rings.
Some rings are toys.
Some toys are dolls.
Conclusions:
I. Some rings are bangles.
II. Some dolls are rings.
