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: I. No R is a G. II. All G’s are H. Conclusions: I. No H is a R. II. No G is a R.
Only conclusion II follows.
Understanding Syllogism Statements and Conclusions
Syllogism questions test your ability to draw logical conclusions based on given statements. You must strictly follow the information provided in the statements, even if it contradicts common knowledge.
Let's analyze the given statements and conclusions.
Analyzing the Statements
We have two statements:
- Statement I: No R is a G.
- Statement II: All G’s are H.
Let's represent these statements. Statement I tells us that there is no overlap between the category 'R' and the category 'G'. They are completely separate. Statement II tells us that the entire category 'G' is contained within the category 'H'. 'G' is a subset of 'H'.
Evaluating the Conclusions
Now, let's evaluate each conclusion based on these statements.
Conclusion I: No H is a R.
- Statement I says "No R is a G".
- Statement II says "All G are H".
- From Statement II, we know that G is inside H. H is a larger circle (or set) that contains the smaller circle (or set) G.
- Statement I tells us that R is completely outside of G.
- However, this doesn't mean R is completely outside of H. H includes G, but it might also include other things that are not G. There is nothing in the statements to prevent R from overlapping with the part of H that is *not* G.
- For example, imagine R are 'Rabbits', G are 'Gray animals', and H are 'Hopping animals'. If "No Rabbits are Gray" (Statement I) and "All Gray animals are Hopping animals" (Statement II), this doesn't automatically mean "No Hopping animals are Rabbits" (Conclusion I). There could be rabbits that are not gray but do hop (e.g., brown rabbits that hop).
Therefore, Conclusion I does not logically follow from the given statements.
Conclusion II: No G is a R.
- Statement I says "No R is a G".
- Conclusion II says "No G is a R".
- These two statements express the same relationship from different perspectives. If it is true that "No R is a G", it must necessarily be true that "No G is a R". This is a principle of logical equivalence for universal negative statements (an E proposition).
Therefore, Conclusion II logically follows directly from Statement I.
Summary of Findings
- Conclusion I ("No H is a R") does not follow.
- Conclusion II ("No G is a R") follows.
Based on this analysis, only Conclusion II follows from the given statements.
The correct option is the one stating that only conclusion II follows.
Revision Table: Syllogism Statement Types
| Type of Statement | Quantifier | Quality | Relation | Example |
|---|---|---|---|---|
| A (Universal Affirmative) | All | Affirmative | Subject is entirely included in Predicate | All cats are mammals. |
| E (Universal Negative) | No | Negative | Subject is entirely excluded from Predicate | No dogs are cats. |
| I (Particular Affirmative) | Some | Affirmative | Subject is partly included in Predicate | Some students are intelligent. |
| O (Particular Negative) | Some... not | Negative | Subject is partly excluded from Predicate | Some birds are not black. |
Additional Information: Conversion in Syllogism
Conversion is a type of immediate inference where the subject and predicate of a statement are swapped. Not all statement types can be converted validly, and the quantity/quality might change for some.
- A statements (All S are P): Converts to an I statement (Some P are S). (e.g., All cats are mammals $\rightarrow$ Some mammals are cats).
- E statements (No S are P): Converts to an E statement (No P are S). This is a simple conversion. (e.g., No dogs are cats $\rightarrow$ No cats are dogs).
- I statements (Some S are P): Converts to an I statement (Some P are S). This is also a simple conversion. (e.g., Some students are intelligent $\rightarrow$ Some intelligent beings are students).
- O statements (Some S are not P): Does not have a valid conversion. (e.g., Some animals are not dogs - cannot validly conclude Some dogs are not animals).
In the given problem, Statement I is "No R is a G" (an E statement). Conclusion II is "No G is a R" (also an E statement, with subject and predicate swapped). This is a valid simple conversion of Statement I, confirming that Conclusion II logically follows from Statement I.
Important Questions from Conventional Syllogism
In this question, three statements followed by two conclusions numbered I and II have been given. You have to take the given statements to be true even if they seem to be at variance from the commonly facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statements: Some flats are apartments.
No apartment is a hall.
Some halls are rooms.
Conclusions: I. At least some rooms are flats.
II. No apartment is a room.
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:
I. Some blue are red.
II. Some green are red.
Conclusions:
I. No blue is green.
II. No red is green.
Given below are two statements, Consider these statements to be true even if they seem factuality absurd, Read the conclusions and then decide which of the given conclusions logically follow(s) from the given statements?
Statements :
1. All vases are flowers.
2. No flowers is a plant.
Conclusions :
1. No vases is a plant.
2. Some plant are vases
In the question two statements are given, followed by three conclusions, I, II and III. You have to consider the statements to be true even if it seems to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements.
Statement 1 : Some cars are scooters.
Statement 2 : All scooters are buses.
Conclusion I : Some scooters are cars.
Conclusion II : Some buses are cars.
Conclusion III : All cars are buses.
In the question below are given three statements followed by two conclusions. You have to take each of the given statements to be true. Read the conclusions and then decide which of the conclusions can be logically derived.
Statements:
Some schools are colleges.
No college is university.
All universities are hospitals.
Conclusions:
I. Some schools are universities.
II. At least some hospitals are colleges.
