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 cabbages are beetroots.
Some cabbages are carrots.
Conclusions:
I. Some beetroots are cabbages.
II. Some beetroots are carrots.
Statements Logic Assessment
This question requires us to evaluate two statements about vegetables and determine if the given conclusions logically follow from these statements. We need to assume the statements are true, regardless of real-world facts.
Statement Logic: Cabbages Beetroot Relationship
Statement 1: All cabbages are beetroots.
This is a universal affirmative statement. It means the entire set of 'cabbages' is contained within the larger set of 'beetroots'. If something is identified as a cabbage, it is automatically also a beetroot.
Symbolically, if $C$ denotes the set of cabbages and $B$ denotes the set of beetroots, this statement can be represented as: $ \forall x (C(x) \implies B(x)) $.
Statement Logic: Cabbages Carrot Overlap
Statement 2: Some cabbages are carrots.
This is a particular affirmative statement. It indicates that there is at least one member that belongs to both the 'cabbages' set and the 'carrots' set. There is an intersection between these two categories.
Symbolically, if $R$ denotes the set of carrots, this statement is: $ \exists x (C(x) \land R(x)) $.
Conclusion I: Beetroots are Cabbages
Conclusion I: Some beetroots are cabbages.
Based on Statement 1 ('All cabbages are beetroots'), we know that every cabbage is also a beetroot. This implies that the set of cabbages is a subset of the set of beetroots. Therefore, it must be true that at least some members of the 'beetroots' set are also members of the 'cabbages' set. This conclusion is a direct logical consequence of Statement 1.
From $ \forall x (C(x) \implies B(x)) $, it directly follows that $ \exists x (B(x) \land C(x)) $. Hence, Conclusion I logically follows.
Conclusion II: Beetroots are Carrots
Conclusion II: Some beetroots are carrots.
We use both statements here. Statement 2 tells us that 'Some cabbages are carrots', meaning there exists at least one entity that is both a cabbage and a carrot. Statement 1 tells us that 'All cabbages are beetroots'. Therefore, any entity that is both a cabbage and a carrot must also be a beetroot (since it is a cabbage). This establishes that there exists at least one entity that is both a beetroot and a carrot.
Combining $ \exists x (C(x) \land R(x)) $ (Statement 2) and $ \forall x (C(x) \implies B(x)) $ (Statement 1), we can deduce $ \exists x (B(x) \land R(x)) $. Hence, Conclusion II logically follows.
Logical Conclusions Validation
After analyzing both statements and evaluating each conclusion based on the rules of logic:
- Conclusion I logically follows from Statement 1.
- Conclusion II logically follows from combining Statement 1 and Statement 2.
Therefore, both conclusions are valid deductions 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 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.
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.
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:
Some figs are orange.
All oranges are grapes.
All mangoes are oranges.
Conclusions:
(I) Some figs are grapes.
(II) All mangoes are grapes.
(III) Some mangoes are figs.
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 shoes are slippers.
All slippers are socks.
All socks are sandals
Conclusions:
(I) Some sandals are slippers
(II) Some socks are shoes.
(III) All sandals are shoes.
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.
