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
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 dancers are talented.
Some girls are dancers.
Conclusions:
I. Some girls are talented.
II. All talented are girls.
III. All girls are talented.
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 directors are actors.
No actor is a producer.
All choreographers are directors.
Conclusions:
I. No choreographer is producer.
II. Some actors are choreographers.
III. No director is a producer.
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 follows from the statements.
Statements:
All lemons are plums.
All plums are dates.
Some dates are mangoes.
Conclusions:
I. Some lemons are mangoes.
II. Some mangoes are plums.
III. All lemons are dates.
IV. Some mangoes are dates.
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 cards are postcards.
Some cards are envelopes.
All envelopes are copies.
Conclusions:
I. Some copies are envelopes.
II. Some postcards are copies.
III. Some cards are copies.
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 employees are tax-payers.
Some employees are farmers.
Some farmers are doctors.
Conclusions:
I. No farmer is a tax-payer.
II. Some farmers are tax-payers.
