In this question, 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 conclusion(s) logically follows/follow from the statements. Statements: Some shirts are pants. All pants are jackets. All jackets are trousers. Conclusions: I. Some trousers are shirts. II. All jackets are shirts.
Only conclusion I follows.
To determine which conclusion logically follows from the given statements, let's analyze each statement and conclusion step-by-step using the rules of syllogism.
Statements Analysis:
- Some shirts are pants. - This implies there is at least one shirt that is also a pant.
- All pants are jackets. - This means every pant is also classified as a jacket.
- All jackets are trousers. - This indicates every jacket is categorized as a trouser.
Conclusion Evaluations:
- Conclusion I: Some trousers are shirts.
- From the statements, we know: Some shirts are pants (Statement 1).
- Those pants are jackets (Statement 2), and all jackets are trousers (Statement 3).
- Thus, some pants (which are originally shirts) can be classified as trousers through these connections.
- Hence, Conclusion I logically follows from the given statements.
- Conclusion II: All jackets are shirts.
- Statement 1 states that only some shirts are pants, not all shirts.
- There is no basis in the statements to infer that every jacket (which includes all pants) will be a shirt.
- Therefore, Conclusion II does not logically follow based on the provided statements.
Therefore, the correct answer is: Only conclusion I follows.
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Consider the following diagrams:
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Consider the following matrix:
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