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:
No chess is a can.
Not a single can is a horn.
Every horn is an adapter.
Conclusions:
I. Some adapters which are horns are chess as well.
II. No chess is a horn.
III. Some adapters are horns.
Understanding the Statements
We are given three statements and three conclusions. Our task is to determine which conclusions logically follow from the statements, assuming the statements are true, even if they contradict common knowledge.
- Statement 1: No chess is a can. (This means the categories 'chess' and 'can' are entirely separate; they have no members in common. Mathematically, Chess ∩ Can = ∅).
- Statement 2: Not a single can is a horn. (This means the categories 'can' and 'horn' are entirely separate. Mathematically, Can ∩ Horn = ∅).
- Statement 3: Every horn is an adapter. (This means the entire category of 'horn' is included within the category of 'adapter'. Mathematically, Horn ⊆ Adapter).
Analyzing the Conclusions
Now, let's examine each conclusion to see if it can be logically derived from the statements.
Conclusion I: Some adapters which are horns are chess as well.
This conclusion suggests that there is an overlap between the group of 'adapters that are horns' and the group of 'chess'. Since Statement 3 tells us that every horn is an adapter, the phrase 'adapters which are horns' simply refers to 'horns'. So, the conclusion is essentially asking if some horns are also chess (Horn ∩ Chess ≠ ∅).
Let's review the statements:
- Chess and Cans are separate.
- Cans and Horns are separate.
- All Horns are Adapters.
The statements establish that chess is separate from cans, and horns are separate from cans. They also state that horns are a type of adapter. However, there is no information given that links chess directly or indirectly (through other categories like 'can' or 'adapter') to horns. It's possible that the set of chess and the set of horns are completely distinct. Because the statements do not force an overlap between chess and horns, this conclusion does not necessarily follow.
Conclusion II: No chess is a horn.
This conclusion claims that the categories 'chess' and 'horn' are mutually exclusive (Chess ∩ Horn = ∅).
Similar to the analysis for Conclusion I, the given statements do not provide enough information to definitively conclude that no chess can be a horn. The 'can' category separates chess from horns, but this separation doesn't prevent chess and horns from overlapping. We can imagine a scenario where these statements are true, but a chess piece could also be classified as a horn:
- Let Chess = {Item A, Item C}
- Let Can = {Item B}
- Let Horn = {Item C}
- Let Adapter = {Item C, Item D}
Checking the statements with this scenario:
- Statement 1: No chess is a can ({Item A, Item C} ∩ {Item B} = ∅) - True.
- Statement 2: No can is a horn ({Item B} ∩ {Item C} = ∅) - True.
- Statement 3: Every horn is an adapter ({Item C} ⊆ {Item C, Item D}) - True.
Now check Conclusion II:
- Conclusion II: No chess is a horn ({Item A, Item C} ∩ {Item C} = {Item C}). Since the intersection is not empty ({Item C}), this conclusion is False in this specific valid scenario.
Because we found a situation where the statements are true but the conclusion is false, Conclusion II does not logically follow.
Conclusion III: Some adapters are horns.
This conclusion states that there exist items that belong to both the 'adapter' category and the 'horn' category (Adapter ∩ Horn ≠ ∅).
Statement 3 says, "Every horn is an adapter" (Horn ⊆ Adapter).
This statement directly implies that if something is a horn, it must also be an adapter. Assuming that the category 'horn' is not empty (i.e., there exists at least one horn), then that horn is automatically an adapter. Therefore, it logically follows that some adapters are indeed horns.
This conclusion is valid.
Final Verdict
After analyzing each conclusion against the provided statements:
- Conclusion I: Does not logically follow.
- Conclusion II: Does not logically follow.
- Conclusion III: Logically follows.
Therefore, the only conclusion that is guaranteed to be true based on the given statements is Conclusion III.
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.
