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.

Question

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.

Prepp Team · Accepted Answer

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.