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.
Only conclusions II and III follow
Understanding Syllogism: Statements and Conclusions
Syllogism questions test your ability to derive logical conclusions from given statements, assuming the statements are true regardless of commonly known facts. We need to analyze the relationships described in the statements and see which of the given conclusions logically follow.
Let's break down the given problem:
Statements:
- Some seeds are fruits.
- Some fruits are jams.
- All jams are desserts.
Conclusions:
- Some jams are seeds.
- Some desserts are jams.
- Some fruits are desserts.
We can use Venn diagrams or logical deduction rules to check each conclusion based on the statements.
Analyzing the Relationships with Venn Diagrams
Let's visualize the statements:
Statement 1: "Some seeds are fruits." This means there is an overlap between the set of seeds and the set of fruits.
Statement 2: "Some fruits are jams." This means there is an overlap between the set of fruits and the set of jams. Note that the fruits that are jams might or might not be the same fruits that are seeds.
Statement 3: "All jams are desserts." This means the set of jams is completely contained within the set of desserts.
Evaluating Each Conclusion
Let's check each conclusion one by one:
Conclusion I: Some jams are seeds.
- We know Some seeds are fruits (S \(\cap\) F \(\neq\) \(\emptyset\))
- We know Some fruits are jams (F \(\cap\) J \(\neq\) \(\emptyset\))
- We know All jams are desserts (J \(\subset\) D)
From "Some seeds are fruits" and "Some fruits are jams", we cannot definitively conclude that "Some jams are seeds". The overlap between seeds and fruits, and the overlap between fruits and jams, might occur in different parts of the 'fruits' category. There is no direct link or guaranteed indirect link established between 'jams' and 'seeds' by the statements. Therefore, this conclusion does not logically follow.
Conclusion II: Some desserts are jams.
- We know All jams are desserts (J \(\subset\) D)
If all elements of the set 'jams' are also elements of the set 'desserts', then there must be some elements in the set 'desserts' that are also in the set 'jams'. This is a direct logical consequence of "All A are B" implies "Some B are A" (assuming B is not empty, which is the standard assumption in syllogism unless stated otherwise). Therefore, this conclusion logically follows.
Conclusion III: Some fruits are desserts.
- We know Some fruits are jams (F \(\cap\) J \(\neq\) \(\emptyset\))
- We know All jams are desserts (J \(\subset\) D)
If some fruits are jams, and every jam is a dessert, then those specific fruits that are jams must also be desserts. So, there are some fruits that are desserts. This conclusion logically follows.
Summary of Conclusions
- Conclusion I: Some jams are seeds. (Does NOT follow)
- Conclusion II: Some desserts are jams. (Follows)
- Conclusion III: Some fruits are desserts. (Follows)
Based on our analysis, only conclusions II and III logically follow from the given statements.
Revision Table: Syllogism Analysis
| Statement/Conclusion | Type | Relationship | Follows? |
|---|---|---|---|
| Some seeds are fruits | Statement | S \(\cap\) F \(\neq\) \(\emptyset\) | Given as true |
| Some fruits are jams | Statement | F \(\cap\) J \(\neq\) \(\emptyset\) | Given as true |
| All jams are desserts | Statement | J \(\subset\) D | Given as true |
| Some jams are seeds | Conclusion I | J \(\cap\) S \(\neq\) \(\emptyset\) | No (Not guaranteed by statements) |
| Some desserts are jams | Conclusion II | D \(\cap\) J \(\neq\) \(\emptyset\) | Yes (If all J are D, then some D are J) |
| Some fruits are desserts | Conclusion III | F \(\cap\) D \(\neq\) \(\emptyset\) | Yes (If some F are J, and all J are D, then some F are D) |
Additional Information: Key Syllogism Rules
Understanding basic rules helps in solving syllogism questions:
- "All A are B" implies "Some A are B" and "Some B are A". (Example: All cats are animals \(\implies\) Some cats are animals, Some animals are cats).
- "No A is B" implies "No B is A", "Some A are not B", and "Some B are not A". (Example: No dog is a cat \(\implies\) No cat is a dog, Some dogs are not cats, Some cats are not dogs).
- "Some A are B" implies "Some B are A". (Example: Some students are boys \(\implies\) Some boys are students).
- "Some A are not B" does NOT imply "Some B are not A". (Example: Some animals are not cats does not mean Some cats are not animals).
- Combining "Some" statements: Two "Some" statements ("Some A are B", "Some B are C") usually do NOT lead to a definite conclusion about "A" and "C".
- Combining "All" and "Some": "All A are B" + "Some B are C" does not guarantee a link between A and C. However, "Some A are B" + "All B are C" implies "Some A are C". (This rule applies to Conclusion III: Some fruits are jams + All jams are desserts \(\implies\) Some fruits are desserts).
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.
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.
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 :
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.
