Introduction / Context:
This is another syllogism question involving relationships between three groups: poets, readers and wise people. The statements tell us how these sets overlap or do not overlap, and we must decide which conclusion logically follows. Such questions demand careful translation of statements like 'No reader is wise' and 'All poets are readers' into simple set relations and then reasoning from them without adding extra assumptions.
Given Data / Assumptions:
- Statement 1: All poets are readers.
- Statement 2: No reader is wise.
- Conclusion 1: No poet is wise.
- Conclusion 2: All readers are poets.
Concept / Approach:
We can treat each group as a set:
- P = set of all poets
- R = set of all readers
- W = set of all wise people
The statement 'All poets are readers' means P ⊆ R. The statement 'No reader is wise' means R and W are disjoint sets (R ∩ W = ∅). We then check which conclusions must always be true given these relations.
Step-by-Step Solution:
Step 1: Translate the statements into set language. 'All poets are readers' means every poet is a reader, so P is a subset of R (P ⊆ R).
Step 2: 'No reader is wise' means there is no person who is both a reader and wise. Hence, R ∩ W = ∅ (the intersection of readers and wise people is empty).
Step 3: Consider Conclusion 1: 'No poet is wise.' Since every poet is a reader (P ⊆ R), and no reader is wise (R ∩ W = ∅), it follows that no poet can be in W. In other words, poets are a subset of readers, and readers have no overlap with wise people, so poets also have no overlap with wise people.
Step 4: Formally, if P ⊆ R and R ∩ W = ∅, then P ∩ W = ∅. This is exactly the content of Conclusion 1: no poet is wise. Therefore, Conclusion 1 must follow.
Step 5: Consider Conclusion 2: 'All readers are poets.' This would mean R ⊆ P. But we are only told that P ⊆ R and nothing about whether every reader must be a poet. It is entirely possible that there are readers who are not poets, such as scientists, engineers or students who read but do not write poetry.
Step 6: Because we can imagine many scenarios where there are readers who are not poets while still satisfying the given statements, Conclusion 2 does not logically follow.
Verification / Alternative check:
Example: Suppose there are 10 readers, of which 3 are poets. All 3 poets are readers, and none of the 10 readers is wise. This satisfies all given statements. Yet not all readers are poets, so Conclusion 2 is false in this valid scenario, confirming that it does not follow.
Why Other Options Are Wrong:
Option A (Neither conclusion follows) is wrong because Conclusion 1 is clearly and directly implied by the given statements.
Option B (Only conclusion 2 follows) is wrong since Conclusion 2 is not supported and can be false even when the statements are true.
Option C (Either 1 or 2 follows) is wrong because only one of them (Conclusion 1) is guaranteed; the other is not.
Common Pitfalls:
A frequent error is to misuse the direction of the subset relation: from 'All poets are readers' some people wrongly conclude 'All readers are poets', which is logically incorrect.
Another mistake is to ignore the implication of 'No reader is wise', which completely excludes readers (and thus poets) from the wise group.
Final Answer:
Since poets are readers and no reader is wise, poets cannot be wise either. Therefore, only conclusion 1 follows.
Discussion & Comments