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.
Syllogism Solution: Analyzing Statements and Conclusions
This problem requires us to analyze the logical relationship between different categories based on given statements and determine which conclusions logically follow.
Understanding the Statements
We are given two statements:
- Statement I: No R is a G. This means there is absolutely no overlap between the category 'R' and the category 'G'. They are completely separate sets.
- Statement II: All G’s are H. This means the entire category 'G' is contained within the category 'H'. Everything that is a G is also necessarily an H.
We must accept these statements as true, regardless of our common knowledge.
Evaluating the Conclusions
We need to check if the following conclusions are necessarily true based only on the given statements.
Conclusion I: No H is a R.
Let's consider the relationship between the categories based on the statements. We know G is entirely inside H (Statement II), and R is entirely separate from G (Statement I). However, Statement II only defines the relationship of G to H. It does not restrict the part of H that is not G.
It is possible that some parts of H (specifically, the parts that are not G) could overlap with R. For example, if H represents 'animals', G represents 'dogs', and R represents 'cats', then Statement I ('No cats are dogs') and Statement II ('All dogs are animals') are true. However, the conclusion 'No animals are cats' (No H is R) is false because cats are animals.
Therefore, Conclusion I does not logically follow from the given statements.
Conclusion II: No G is a R.
Statement I explicitly states, "No R is a G". This establishes a mutual exclusion between categories R and G. If no member of R is a member of G, then it is logically equivalent and necessary that no member of G can be a member of R. The relationship of being disjoint is symmetrical.
Therefore, Conclusion II logically follows directly from Statement I.
Determining Which Conclusion Follows
Based on our analysis:
- Conclusion I (No H is a R) does not follow.
- Conclusion II (No G is a R) follows.
Thus, only conclusion II logically follows from the given statements.
Syllogism Analysis Revision Table
| Statement/Conclusion | Type | Relationship Implied | Logically Follows? | Reasoning |
|---|---|---|---|---|
| Statement I: No R is G | Universal Negative (E) | R and G are disjoint sets | N/A | Given premise |
| Statement II: All G are H | Universal Affirmative (A) | G is a subset of H | N/A | Given premise |
| Conclusion I: No H is R | Universal Negative (E) | H and R are disjoint sets | No | Statement II doesn't restrict parts of H not in G from overlapping with R. |
| Conclusion II: No G is R | Universal Negative (E) | G and R are disjoint sets | Yes | Directly equivalent to Statement I ("No R is a G"). |
Additional Information on Syllogisms and Logic
Syllogisms are fundamental in deductive reasoning. They consist of premises (statements) and a conclusion. The goal is to determine if the conclusion is necessarily true if the premises are assumed to be true.
Categorical syllogisms involve statements that relate categories (or sets). The four standard types of categorical statements, often denoted by vowels, are:
- A: All S are P (Universal Affirmative)
- E: No S is P (Universal Negative)
- I: Some S are P (Particular Affirmative)
- O: Some S are not P (Particular Negative)
Visual tools like Venn diagrams can be very helpful in solving these types of problems. You draw circles representing each category and shade or mark regions based on the statements to see what regions must be empty or must contain members. If the conclusion's relationship is guaranteed by the diagram based on the statements, it follows logically.
Statement I ("No R is a G") means the overlap area between R and G is empty. Statement II ("All G's are H") means the area of G outside H is empty. When you combine these, the area where G and R overlap is empty, and all of G is within H. The critical insight for Conclusion I is that there's still an area within H (the part not covered by G) whose relationship with R is not specified by the statements, allowing for potential overlap.
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.
