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 conclusions logically follows/follow from the statements. Statements: I. No streak is a line. II. Some lines are bands. III. All bands are flashes. Conclusions: I. Some flashes are streaks. II. No flash is a line.
Neither conclusion I nor II follows
Detailed Syllogism Solution: Analyzing Statements and Conclusions
This question asks us to analyze given statements and determine which of the provided conclusions logically follow from them. We must assume the statements are true, regardless of whether they align with real-world knowledge. This type of problem tests our ability in logical deduction, a key part of syllogism.
Understanding the Statements
Let's break down the given statements:
- Statement I: No streak is a line. This establishes a complete separation between the category 'streak' and the category 'line'. If something is a streak, it cannot be a line, and vice versa.
- Statement II: Some lines are bands. This indicates an overlap or intersection between the category 'line' and the category 'band'. There exists at least one entity that is both a line and a band.
- Statement III: All bands are flashes. This means the entire category of 'bands' is contained within the category of 'flashes'. If something is a band, it must also be a flash.
Evaluating the Conclusions
Now, let's evaluate each conclusion based on the statements.
Conclusion I: Some flashes are streaks.
To see if this conclusion follows, we need to find a connection between 'flashes' and 'streaks' based on the statements.
- From Statement I, we know 'streaks' and 'lines' are completely separate.
- From Statements II and III, we know that 'some lines are bands' and 'all bands are flashes'. Combining these, if some lines are bands, and all bands are flashes, then it logically follows that some lines are flashes.
We have a relationship between 'lines' and 'flashes' ('Some lines are flashes'), and a relationship between 'streaks' and 'lines' ('No streak is a line'). However, we have no direct link between 'streaks' and 'flashes'. The statements don't provide information about whether the 'flashes' that are *not* lines have any overlap with 'streaks'. It's possible that flashes only overlap with lines, or with things that are neither lines nor streaks. Therefore, we cannot definitively conclude that some flashes are streaks.
Conclusion II: No flash is a line.
To evaluate this conclusion, let's again look at the connections between 'flashes' and 'lines'.
- Statement II says: Some lines are bands. (Some L are B)
- Statement III says: All bands are flashes. (All B are F)
Using these two statements, we can deduce a relationship between Lines and Flashes. If there are some lines that are bands (Statement II), and everything that is a band is also a flash (Statement III), then those 'some lines' that are bands must also be flashes. Therefore, it logically follows that some lines are flashes.
Conclusion II states that "No flash is a line", which means 'flashes' and 'lines' are completely separate. However, our deduction from statements II and III shows that there is an overlap; some lines *are* flashes (and therefore, some flashes are lines). Since Conclusion II contradicts the logical deduction from the statements, it does not follow.
Summary of Evaluation
- Conclusion I: Some flashes are streaks. — Does not follow.
- Conclusion II: No flash is a line. — Does not follow (contradicts 'Some lines are flashes').
Based on the analysis, neither conclusion logically follows from the given statements.
Revision Table: Key Syllogism Concepts
| Statement Type | Notation Example | Relationship |
|---|---|---|
| All A are B | \(A \subset B\) | A is a subset of B |
| No A is B | \(A \cap B = \emptyset\) | A and B are mutually exclusive |
| Some A are B | \(A \cap B \neq \emptyset\) | There is an overlap between A and B |
| Some A are not B | \(A \setminus B \neq \emptyset\) | There are elements in A that are not in B |
Additional Information: Solving Syllogism Problems
Syllogism problems require careful logical reasoning. Here are some tips:
- Assume Statements are True: Treat the statements as absolute facts within the context of the problem, even if they seem illogical in the real world.
- Visualize Relationships: Using Venn diagrams can be very helpful. Draw circles representing the categories (streak, line, band, flash) and show the relationships described by the statements (separation, overlap, containment).
- Combine Statements: Look for ways to combine two statements to deduce a relationship between categories that weren't directly linked initially (like how we combined Statements II and III to link lines and flashes).
- Avoid Outside Knowledge: Do not use any information or common knowledge outside of the provided statements.
- Test Each Conclusion: Rigorously check if each conclusion is *necessarily* true based *only* on the statements. If there is any possibility, however remote, that the conclusion could be false given the statements, then it does not follow.
This structured approach helps ensure you rely purely on the given logic to solve syllogism questions.
Similar Questions
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.
Three 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:
All pens are newspapers.
Some newspapers are novels.
No novel is a book.
Conclusions:
I. Some books are pens.
II. Some novels are pens.
III. No book is a pen.
Three 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 spices are medicines.
All medicines are chemicals.
No chemical is cheap.
Conclusions:
I. Some medicines are cheap.
II. Some chemicals are spices.
III. No medicine is cheap.
Three 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:
All oranges are apples.
Some oranges are bananas.
All bananas are fruits.
Conclusions:
I. Some fruits are apples.
II. Some apples are bananas.
III. Some oranges are fruits.
Select the Venn diagram that best illustrates the relationship between the following classes.
Swimming, Running, Sports
Select the Venn diagram that best illustrates the relationship between the following classes.
Dialect, Language, Communication
Three 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 seeds are fruits.
Some fruits are jams.
All jams are desserts.
Conclusions:
I. Some jams are seeds.
II. Some desserts are jams.
III. Some fruits are desserts.
Three 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 :
All stars are moons.
Some moons are suns.
All suns are satellites.
Conclusions :
I. Some satellites are moons.
II. Some satellites are stars.
III. Some moons are stars.
Three statements are followed by three conclusions numbered I, II and III. You have to consider these statements to be true, even if they seem to be at variance with commonly known facts. Decide which of the given conclusions logically follow(s) from the given statements.
Statements:
All tools are spanners.
Some spanners are utensils.
No spanner is an iron.
Conclusions:
(I) Some tools are irons.
(II) Some utensils are tools.
(III) Some utensils are not iron.
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.
