Statements:
All calculators are dustbins.
All complexes are dustbins.
Some adamants are cameras.
Conclusions:
I. Some calculators are complexes.
II. Some dustbins are calculators.
III. Some dustbins are adamants.
Statements Analysis
We are given three initial statements and need to determine which conclusions logically follow from them. Let's break down each statement:
Statement 1: All calculators are dustbins.
This statement establishes a relationship where the category 'calculators' is entirely included within the category 'dustbins'. Using set notation, if C represents the set of calculators and D represents the set of dustbins, this statement means $C \subseteq D$. In logical terms, if something is a calculator, it must be a dustbin.
Statement 2: All complexes are dustbins.
Similarly, this statement indicates that the category 'complexes' is entirely included within the category 'dustbins'. If K represents the set of complexes, this means $K \subseteq D$. If something is a complex, it must also be a dustbin.
Statement 3: Some adamants are cameras.
This statement tells us there is an overlap between the category 'adamants' and the category 'cameras'. It means at least one adamant is a camera, or at least one camera is an adamant. If A represents adamants and Cam represents cameras, this means $A \cap Cam \neq \emptyset$. This statement does not connect adamants or cameras to calculators, complexes, or dustbins.
Conclusions Analysis
Now, let's evaluate each conclusion based on the information provided in the statements.
Conclusion I: Calculators & Complexes Link
The conclusion is: Some calculators are complexes. ($C \cap K \neq \emptyset$)
- From Statement 1, we know all calculators are dustbins ($C \subseteq D$).
- From Statement 2, we know all complexes are dustbins ($K \subseteq D$).
- Both calculators (C) and complexes (K) are subsets of dustbins (D). However, these statements do not provide any information about whether the sets C and K overlap. They could be completely separate subsets within D, or they could overlap.
- Therefore, we cannot logically conclude that some calculators are complexes. This conclusion does not follow.
Conclusion II: Dustbins & Calculators Link
The conclusion is: Some dustbins are calculators. ($D \cap C \neq \emptyset$)
- Statement 1 explicitly states: "All calculators are dustbins" ($C \subseteq D$).
- If every single calculator is a dustbin, it logically follows that the group of 'dustbins' must contain members that are 'calculators'.
- Therefore, there are indeed dustbins that are calculators. This conclusion logically follows.
Conclusion III: Dustbins & Adamants Link
The conclusion is: Some dustbins are adamants. ($D \cap A \neq \emptyset$)
- Statement 3 mentions 'adamants' and 'cameras' ($A \cap Cam \neq \emptyset$).
- Statements 1 and 2 relate 'calculators' and 'complexes' to 'dustbins'.
- There is no information provided in any of the statements that links 'adamants' (or 'cameras') to 'dustbins'.
- Therefore, we cannot logically conclude that some dustbins are adamants. This conclusion does not follow.
Final Determination
Based on the analysis, only Conclusion II logically follows from the given statements. The relationship $C \subseteq D$ directly supports the conclusion that some members of D are also members of C.
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.
