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
- 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 tables are chairs.
II. All desks are chairs.
III. No chair is a fan.
Conclusions:
I. Some desks are tables.
II. Some fans are desks. - 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. All tables are charts.
II. Some charts are graphs.
III. Some graphs are pies.
Conclusions:
I. No table is a graph.
II. Some pies are charts. - 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:
All boxes are squares.
All squares are rectangles.
All rectangles are figures.
Conclusions:
I. All boxes are figures.
II. All squares are figures. 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 given conclusions logically follow(s) from the statements.
Statements:
Some fractions are marts.
No mart is a stud.
All studs are frogs.
Conclusions:
I. Some fractions are definitely not studs.
II. Some fractions are definitely not marts.
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 calculators are lanterns.
Some lanterns are mobiles.
Conclusions:
I. All mobiles are calculators.
II. No mobile is a lantern.
III. Some mobiles are lanterns.
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 parrots are crows.
All crows are eagles.
Conclusions:
I. All parrots are eagles.
Il. Some crows are parrots.
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 from the statements.
Statements:
No certificate is a paper.
All pens are papers.
Conclusions:
I. No certificate is a pen.
II. No paper is a certificate.
III. Some papers are pens.
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 officers are clerks.
All clerks are workers.
Conclusions:
I. Some workers are officers.
Il. No worker is an officer.
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 chargers are phones.
No phone is a watch.
Conclusions:
I. All phones are chargers.
Il. No charger is a watch.
Ill. No watch is a phone.
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 wallets are bags.
Some bags are envelopes.
Conclusions:
I. Some wallets are envelopes.
II. No wallet is an envelope.
III. No bag is an envelope.
Important Questions from Syllogism
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 students are players.
All players are male.
Conclusions:
I. All males are players.
II. Some males are students.
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:
No creative is an employer.
All experts are creative.
All workers are experts.
Conclusions:
I. No employer is an expert.
II. No worker is an employer.
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 actors are choreographers.
All choreographers are producers.
Not a single producer is a director.
Conclusions:
I. Some actors are directors.
II. Not a single actor is a director.
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 :
1. All flowers are tulips.
2. No tulips are whites.
Conclusions :
I. All tulips are flowers.
II. Some tulips are whites.
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 rats are dogs.
Some rats are hens.
Conclusions:
I. Some rats are dogs.
II. Some hens are rats.
