Two statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: Some books are novels. No novel is a diary. Conclusions: I. No book is a diary. II. All diaries are books. III. No diary is a novel.
Only conclusion III follows
Analyzing Syllogism: Books, Novels, and Diaries
This question requires us to determine which of the given conclusions logically follow from the two statements, assuming the statements are true.
Understanding the Statements
We are given two statements:
- Some books are novels.
- No novel is a diary.
Let's represent these relationships using Venn diagrams to visualize the overlap and separation between the categories: Books, Novels, and Diaries.
- "Some books are novels" means there is an overlap between the set of Books and the set of Novels. Some elements are common to both sets.
- "No novel is a diary" means there is absolutely no overlap between the set of Novels and the set of Diaries. These two sets are mutually exclusive.
Combining these, we know that the part of the 'Books' set that overlaps with 'Novels' cannot overlap with 'Diaries'. However, the part of the 'Books' set that does *not* overlap with 'Novels' could potentially overlap with 'Diaries'.
Evaluating the Conclusions
Now let's examine each conclusion based on the given statements and our understanding of their relationships.
Conclusion I: No book is a diary.
This conclusion states that there is no overlap between the set of Books and the set of Diaries. From the statements, we know that no *novel* is a diary, and some books are novels. This means the books that are novels cannot be diaries. However, the statements do not provide any information about the books that are *not* novels. It is possible that some books that are not novels are diaries. Therefore, we cannot conclude that no book is a diary based solely on the given statements. This conclusion does not logically follow.
Conclusion II: All diaries are books.
This conclusion states that the set of Diaries is entirely contained within the set of Books. The statements tell us about the relationship between books and novels, and between novels and diaries. They provide no information about the relationship between diaries and books. There is nothing in the statements that suggests all diaries must be books. Therefore, this conclusion does not logically follow.
Conclusion III: No diary is a novel.
This conclusion states that there is no overlap between the set of Diaries and the set of Novels. The second statement explicitly says, "No novel is a diary." If no novel is a diary, it logically follows that no diary can be a novel. This is the contrapositive of the second statement, and it is always true if the original statement is true. Therefore, this conclusion logically follows from the statements.
Summary of Conclusions
Based on our analysis:
- Conclusion I ("No book is a diary") does not follow.
- Conclusion II ("All diaries are books") does not follow.
- Conclusion III ("No diary is a novel") logically follows.
Only conclusion III is valid based on the given statements.
| Statement | Relationship |
|---|---|
| Some books are novels. | Partial overlap (Books & Novels) |
| No novel is a diary. | No overlap (Novels & Diaries) |
| Conclusion | Analysis | Follows? |
|---|---|---|
| I. No book is a diary. | Statements don't exclude possibility of non-novel books being diaries. | No |
| II. All diaries are books. | Statements provide no info on relationship between Diaries and Books. | No |
| III. No diary is a novel. | Directly follows from "No novel is a diary". | Yes |
Revision Table: Syllogism Fundamentals
| Term | Explanation |
|---|---|
| Statement | A premise assumed to be true for the purpose of the argument. |
| Conclusion | A proposition derived from the statements. |
| Syllogism | A form of deductive reasoning where a conclusion is drawn from two or more premises. |
| Logically Follows | A conclusion is logically valid if it must be true whenever the statements are true. |
| Contrapositive | Flipping and negating a statement. "No A is B" implies "No B is A". |
Additional Information: Syllogism and Logical Reasoning
Syllogism questions are common in logical reasoning sections of exams. They test your ability to draw valid conclusions based *only* on the information provided in the statements, even if those statements contradict real-world knowledge. It's crucial not to use outside information.
Standard forms of syllogisms involve quantified statements like "All A are B", "No A is B", "Some A are B", and "Some A are not B". Visualizing these relationships with Venn diagrams can be a helpful technique to check the validity of conclusions.
In this specific syllogism, the relationship "No novel is a diary" is a strong exclusion. Any element that is a novel cannot be a diary, and vice-versa. The "Some books are novels" statement introduces a partial relationship, meaning part of the 'Books' category is also part of the 'Novels' category. The key is to understand that "some" does not imply "all" or "only some". It just means there is at least one element common to both sets.
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.
