In the following questions, two statements S1 & S2 are given followed by two conclusions I & II. Taking the two statements S1 and S2 as true, decide which one of the answer (A), (B), (C), (D) logically follows.
Statements : S1 : All girls are engineers. S2 : All travellers are girls. Conclusions : I : All travellers are engineers. II : All girls are travellers.
Only I follows.
Syllogism Question Solution: Statements and Conclusions Analysis
In this logical reasoning question, we are given two statements, S1 and S2, and two conclusions, I and II. Our task is to determine which of the conclusions logically follows from the given statements, assuming the statements are true. This type of problem is commonly known as a syllogism, where we deduce new information from provided premises.
Statements Analysis for Syllogism
Let's carefully examine the provided statements:
- Statement S1: All girls are engineers. This statement implies that the set of 'girls' is entirely included within the set of 'engineers'. If someone is a girl, they must also be an engineer. However, it does not mean that all engineers are girls; there could be other individuals who are engineers but are not girls.
- Statement S2: All travellers are girls. This statement means that the set of 'travellers' is entirely included within the set of 'girls'. If someone is a traveller, they must also be a girl. Similar to S1, it does not mean that all girls are travellers; there could be girls who are not travellers.
We can visualize these relationships using set notation or mentally represent them like Venn diagrams:
| Concept | Relationship |
|---|---|
| S1: Girls and Engineers | Girls \( \subseteq \) Engineers |
| S2: Travellers and Girls | Travellers \( \subseteq \) Girls |
By combining these two statements, we establish a clear chain of inclusion:
Travellers \( \subseteq \) Girls \( \subseteq \) Engineers
This means if something is a traveller, it is automatically a girl. And if it is a girl, it is automatically an engineer. This chain helps us evaluate the conclusions effectively.
Conclusions Evaluation for Syllogism
Now, let's evaluate each conclusion based on our analysis of the statements and the derived chain of inclusion.
Conclusion I: All travellers are engineers.
- From statement S2, we know that all travellers are girls. This establishes a direct link from travellers to girls.
- From statement S1, we know that all girls are engineers. This establishes a direct link from girls to engineers.
- Combining these two logical steps: If a person is a traveller, they must be a girl (from S2). Since all girls are engineers (from S1), that traveller must also logically be an engineer.
- Therefore, this conclusion logically follows from the given statements.
Conclusion II: All girls are travellers.
- Statement S2 tells us that all travellers are girls. This means the group of 'travellers' is a subset of the group of 'girls'.
- However, this statement does not imply the reverse. It does not state that every single girl is also a traveller. There could be many girls who do not travel. For example, some girls might prefer staying at home, and thus would not be considered travellers.
- The statement "All A are B" does not automatically mean "All B are A."
- Therefore, this conclusion does not logically follow from the given statements.
Logical Deduction from Syllogism Statements
Based on our thorough analysis of both statements and conclusions:
- Conclusion I (All travellers are engineers) is logically sound because the statements create a clear transitive relationship: Travellers lead to Girls, and Girls lead to Engineers, thus Travellers lead to Engineers.
- Conclusion II (All girls are travellers) is not necessarily true as the statements only provide a one-way inclusion from travellers to girls, not the reverse.
Therefore, only Conclusion I is a valid deduction from the given premises.
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.
