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: All lotuses are roses. All lotuses are hibiscuses. Conclusions: I. All roses are hibiscuses. II. Some hibiscuses are lotuses. III. Some roses are hibiscuses.
Analyzing Syllogism Statements on Lotuses, Roses, and Hibiscuses
This question requires us to evaluate logical conclusions derived from two given statements. This is a typical syllogism problem where we must determine which conclusions necessarily follow from the premises, assuming the premises are true.
Understanding the Given Statements
We are presented with the following two statements:
- Statement 1: All lotuses are roses.
- This implies that the entire set of 'lotuses' is included within the set of 'roses'. If any flower is a lotus, it is automatically also a rose.
- Statement 2: All lotuses are hibiscuses.
- Similarly, this implies that the entire set of 'lotuses' is included within the set of 'hibiscuses'. If any flower is a lotus, it is automatically also a hibiscus.
Combining these, we understand that the category 'lotuses' is a subset of both 'roses' and 'hibiscuses'. Any entity identified as a lotus must possess the characteristics of both a rose and a hibiscus according to these statements.
Analyzing the Conclusions
Let's examine each conclusion based on the logic derived from the statements:
Conclusion I: All roses are hibiscuses.
To assess this, consider the relationship derived: All Lotuses are Roses (L ⊆ R) and All Lotuses are Hibiscuses (L ⊆ H).
- This conclusion suggests that the set of 'roses' is entirely contained within the set of 'hibiscuses' (R ⊆ H).
- However, the statements do not provide enough information to support this. While all lotuses are both roses and hibiscuses, there could be other roses that are not lotuses, and these roses might not be hibiscuses. The statements only guarantee properties related to lotuses.
- Therefore, Conclusion I does not logically follow from the given statements.
Conclusion II: Some hibiscuses are lotuses.
This conclusion relates hibiscuses to lotuses.
- Statement 2 states: "All lotuses are hibiscuses."
- If we accept that lotuses exist (which is standard in syllogistic logic unless stated otherwise), then this statement directly means that those existing lotuses are a part of the group of hibiscuses.
- Hence, it is logically true that at least some hibiscuses are lotuses. This is a valid conversion of a universal affirmative statement ("All A are B") to a particular affirmative statement ("Some B are A"), assuming A exists.
- Therefore, Conclusion II logically follows.
Conclusion III: Some roses are hibiscuses.
This conclusion explores the overlap between roses and hibiscuses.
- We know from Statement 1 that all lotuses are roses (L ⊆ R).
- We know from Statement 2 that all lotuses are hibiscuses (L ⊆ H).
- If lotuses exist, then these lotuses are members of both the 'roses' category and the 'hibiscuses' category. This means there is an overlap between roses and hibiscuses, specifically where the lotuses reside.
- Therefore, it is logically true that at least some roses are hibiscuses.
- Conclusion III logically follows.
Summary of Logical Flow
Based on the analysis of each conclusion:
- Conclusion I: Does not follow.
- Conclusion II: Follows.
- Conclusion III: Follows.
The set of conclusions that logically follow from the given statements are II and III.
Similar Questions
Two 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 follow(s) from the statements.
Statements:
No book is a novel.
All novels are diaries.
Conclusions:
I. All diaries can never be books.
II. Some books are diaries.
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 rhombuses are tangents.
All chords are tangents.
Conclusions:
I. Some rhombuses being chords is a possibility.
II. Some tangents are rhombuses.
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 C are P.
No C is a T.
All P are S.
Conclusions :
I. All S being C is a possibility.
II. At least some T are not C.
III. Some P are not T's.
Three statements are followed by three conclusions numbered I, II, 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 follows from the given statements.
Statements :
No Mango is a banana.
No banana is a guava.
Some guavas are oranges.
Conclusions :
(I) Some mangoes are oranges.
(II) Some guavas are mangoes.
(III) No orange is a banana.
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 tigers are fishes.
No elephant is a tiger.
Some deer are tigers.
Conclusions:
I. Some fishes are deer.
II. No elephant is a deer.
III. No deer is a fish.
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.
Statement :
All Bananas are Grapes.
All Papayas are Pineapple.
Some Pineapples are Banana.
Conclusions:
(I) Some Papayas are Grapes.
(II) Some Grapes are Pineapples.
(III) Some Bananas are Papayas.
Two 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 follow(s) from the statements.
Statements:
All cups are saucers.
No saucer is a plate.
Conclusions:
I. Some cups are plates.
II. No cup is a plate.
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 cubs are trucks.
All trucks are lanterns.
No lanterns are bricks.
Conclusions:
I. Some cubs are lanterns.
II. Some trucks are not bricks.
III. All cubs are trucks.
Two 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 follow(s) from the statements.
Statements:
No locks are keys.
Some keys are passwords.
Conclusions:
I. Some passwords are locks.
II. All passwords are locks.
Two 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 follow(s) from the statements.
Statements:
Some defects are problems.
Some problems are solutions.
Conclusions:
I. Some defects being solutions is a possibility.
II. No solution is a defect.
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.
