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. Some bamboos are sticks. II. All canes are sticks. III. All canes are twigs. Conclusions: I. Some bamboos are twigs. II. Some twigs are sticks.
Logical Analysis of Statements and Conclusions
This question requires us to evaluate logical conclusions based on a set of given statements. We need to determine if the conclusions necessarily follow from the statements, assuming the statements are true.
Analyzing the Statements
Let's break down each statement and understand the relationship between the categories mentioned:
- Statement I: Some bamboos are sticks. This means there is at least one bamboo that is also a stick. In set notation, if B represents the set of bamboos and S represents the set of sticks, then the intersection is not empty: $B \cap S \neq \emptyset$.
- Statement II: All canes are sticks. This means the entire set of canes is included within the set of sticks. If C represents the set of canes, then $C \subset S$.
- Statement III: All canes are twigs. This means the entire set of canes is also included within the set of twigs. If T represents the set of twigs, then $C \subset T$.
Evaluating the Conclusions
Now, let's examine each conclusion based on the information from the statements:
-
Conclusion I: Some bamboos are twigs.
Statement I tells us about the relationship between bamboos and sticks ($B \cap S \neq \emptyset$). Statements II and III link canes to sticks and twigs ($C \subset S$ and $C \subset T$). However, there's no information connecting bamboos directly or indirectly to twigs. It's possible that the bamboos which are sticks are not twigs, and the twigs (which include canes) are separate from these specific bamboos. Therefore, this conclusion does not necessarily follow from the given statements.
-
Conclusion II: Some twigs are sticks.
From Statement II, we know that all canes are sticks ($C \subset S$). From Statement III, we know that all canes are twigs ($C \subset T$). Since the set of canes (C) is a subset of both the set of sticks (S) and the set of twigs (T), it means that any member of the set C is both a stick and a twig. Assuming there exists at least one cane (the sets are not empty), then there must be entities that are both twigs and sticks. Therefore, the statement "Some twigs are sticks" logically follows. In set notation, since $C \subset S$ and $C \subset T$, their intersection $S \cap T$ contains C, meaning $S \cap T \neq \emptyset$.
Logical Deduction Summary
We established the following relationships:
- Bamboos and Sticks have some overlap.
- Canes are entirely within Sticks.
- Canes are entirely within Twigs.
From these, we can see that the category 'Canes' serves as a link. Since all canes are twigs and all canes are sticks, the category 'Twigs' must contain entities (namely, canes) that are also 'Sticks'. This validates Conclusion II.
However, the overlap between 'Bamboos' and 'Sticks' doesn't guarantee any overlap with 'Twigs'. The 'bamboos' that are 'sticks' could exist in a part of the 'sticks' category that does not overlap with the 'twigs' category (which contains 'canes').
Final Determination
Based on the logical analysis, only Conclusion II necessarily follows from the given statements.
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:
Some defects are problems.
Some problems are solutions.
Conclusions:
I. Some defects being solutions is a possibility.
II. No solution is a defect.
Given below are two statements and two conclusions. Take the statements to be true even if they are at variance with commonly known facts, and decide whether the conclusion(s) follow(s) the given statements.
Statements:
Some bags are sacks.
Some sacks are juts.
Conclusions:
I. Some bags are juts.
II. Some juts are sacks.
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 boxes are pins.
All pins are taps.
No tap is a star.
Conclusions:
I. All boxes are pins.
II. Some taps are pins.
III. Some stars are not taps.
Two statements are given, followed by two conclusions numbered I and II. Taking the statements to be true, even if they seem to be at variance from commonly known facts, decide which of the conclusions logically follows from the statements.
Statements:
All cycles are buses.
Some buses are trains.
Conclusions:
I. No cycle is train.
II. All cycles are trains.
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.
