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
- Consider the following Statements and Conclusions :
Statements : Mohan is a good sportsman.
Sportsmen are healthy.
Conclusions : I. All healthy persons are sportsmen.
II. Mohan is healthy.
Which one of the following is correct? Premises : All metals are grey in colour. Some metals are heavy.
Conclusion: I. All heavy metals are grey in colour.
II. All light metals are not grey in colour.Premises : All film stars are playback singers. All film directors are film stars.
Conclusion: I. All film directors are playback singers.
II. Some film stars are film directors.Premises : All apples are golden in colour. No golden coloured things are cheap.
Conclusion: I. All apples are cheap.
II. Golden coloured apples are not cheap.Read the given statement and conclusions carefully. Assuming that the information given in the statement 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 statement.
Statement:
All reds are black.
Conclusions:
1. Some blacks are red.
2. Some reds are black.
