In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements. Statements: I. All T are G. II. All G are H. Conclusions: I. All T are H. II. No G is T. III. All H are G.
Only conclusion I follows
Understanding Statements and Conclusions
This question asks us to analyze a set of statements and determine which of the given conclusions logically follow from these statements. This type of problem is common in logical reasoning and is often referred to as syllogism. We must accept the statements as true, even if they contradict general knowledge, and then evaluate the conclusions based *only* on these statements.
Analyzing the Given Statements
We are given two statements:
- Statement I: All T are G.
- Statement II: All G are H.
These statements describe relationships between three categories or sets: T, G, and H.
- Statement I tells us that the set of 'T' is completely contained within the set of 'G'. Every member of T is also a member of G.
- Statement II tells us that the set of 'G' is completely contained within the set of 'H'. Every member of G is also a member of H.
We can visualize this relationship using Venn diagrams. If all T are G, and all G are H, it creates a hierarchy where T is inside G, and G is inside H. This means T is nested within G, and G is nested within H.
Evaluating the Given Conclusions
Now, let's examine each conclusion based on the truth of the given statements:
- Conclusion I: All T are H.
Based on our analysis of the statements, if all T are G (Statement I), and all G are H (Statement II), then anything that is in T must first be in G, and since everything in G is in H, anything in T must also be in H. This conclusion logically follows from the two statements. It's like saying if all apples are fruits, and all fruits are food, then all apples are food.
- Conclusion II: No G is T.
Statement I clearly states "All T are G". This implies that there are indeed items that are both T and G (specifically, all the items that are T are also G). Therefore, the conclusion "No G is T" directly contradicts Statement I and is false.
- Conclusion III: All H are G.
Statement II says "All G are H". This means G is a subset of H. However, it does not necessarily mean that H is a subset of G. There could be elements in H that are not in G. For example, if G represents "dogs" and H represents "animals", it's true that all dogs are animals, but it's not true that all animals are dogs (there are cats, birds, etc., which are animals but not dogs). So, this conclusion does not logically follow from the statements.
Summary of Conclusion Analysis
Let's summarize our findings:
- Conclusion I: All T are H - Follows
- Conclusion II: No G is T - Does not follow
- Conclusion III: All H are G - Does not follow
Only Conclusion I logically follows from the given statements.
Final Answer Selection
Based on the analysis, only Conclusion I is valid. We need to select the option that states this.
Looking at the options:
- Option 1: All conclusion follows (Incorrect, only I follows)
- Option 2: Only conclusion III follows (Incorrect, III does not follow)
- Option 3: Only conclusion I follows (Correct)
- Option 4: Only conclusion II follows (Incorrect, II does not follow)
Therefore, the correct option is the one stating that only conclusion I follows.
| Statement | Relationship | Implication |
|---|---|---|
| I. All T are G | T is a subset of G | Every T is a G |
| II. All G are H | G is a subset of H | Every G is an H |
| Conclusion | Validity | Reasoning |
|---|---|---|
| I. All T are H | Valid | Since T is in G, and G is in H, T must be in H. |
| II. No G is T | Invalid | Statement I says "All T are G", directly implying some Gs are Ts. |
| III. All H are G | Invalid | "All G are H" does not mean "All H are G". H could contain things not in G. |
Revision Table: Syllogism Basics
| Concept | Explanation | Example |
|---|---|---|
| Statement | A premise accepted as true for the purpose of the argument. | All cats are mammals. |
| Conclusion | A proposition inferred from the statements. | Therefore, my pet Felix is a mammal (if Felix is a cat). |
| Follows Logically | The conclusion must be true IF the statements are true. | If A is B, and B is C, then A logically follows to be C. |
| Syllogism | A form of logical reasoning where a conclusion is derived from two or more statements. | Statements: All M are N. All N are P. Conclusion: All M are P. |
Additional Information: Types of Statements in Syllogism
Statements in syllogism problems typically fall into four categories based on their quantity (Universal/Particular) and quality (Affirmative/Negative):
- Universal Affirmative (A): All S are P (e.g., All dogs are animals).
- Universal Negative (E): No S is P (e.g., No fish are birds).
- Particular Affirmative (I): Some S are P (e.g., Some students are athletes).
- Particular Negative (O): Some S are not P (e.g., Some animals are not dogs).
The statements in this question ("All T are G", "All G are H") are both Universal Affirmative (A type) statements. Understanding these types helps in analyzing the relationships and drawing valid conclusions in logical reasoning problems involving statements and conclusions.
Similar Questions
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:
All pencils are colours.
All colours are paints.
Some paints are drawings.
Conclusions:
I. Some pencils are drawings.
II. Some paints are colours.
III. Some colours are pencils
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:
All plates are bowls.
No bowl is a glass.
Some glasses are vessels.
Conclusions:
I. Some glasses are plates.
II. Some bowls are plates.
III. Some vessels are bowls.
Three statements are given followed by three conclusions numbered I, Il and lII. 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 fruits are wines.
Some wines are juices.
All juices are alcohols.
Conclusions:
I. Some alcohols are juices.
Il. Some wines are alcohols.
III. Some wines are fruits.
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 rugs are blankets.
2. All blankets are pillows.
3. Some blankets are frames.
Conclusions:
I. All pillows are rugs.
II. Some pillows are rugs.
III. All rugs are frames
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 polygons are angles.
All angles are diagonals.
All cones are cubes.
All cubes are decagons.
No diagonal is a cube.
Conclusions:
I. Some diagonals are polygons.
II. All diagonals are decagons.
III. No polygon is a cone.
IV. Some cubes are angles.
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:
All reds are pinks.
All whites are pinks.
All pinks are oranges.
Conclusions:
I. All whites are oranges.
II. All oranges are reds.
III. Some oranges are whites.
In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. All R are M.
II. All L are M.
Conclusions:
I. Some M are not R.
II. Some L are R.
III. Some M are L.
In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. All M are A.
II. No A is R.
Conclusion:
I. No M is R.
II. Some A are M.
III. Some R are A.
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 follow(s) from the statements.
Statements:
All c are f.
No f is t.
All p are c.
Conclusions:
I. Some t are c.
II. No p is t.
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 Tim are Jack.
No Jack is Ben.
Some Ben is Ruth.
Conclusions:
I. No Ruth is Jack.
II. Some Ben are Jack.
III. No Ben is Tim.
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 following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. All A are S.
II. No D is A.
Conclusions:
I. Some S are A.
II. All S are D.
III. No A is D.
In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. Some land are hard.
II. No stone is land.
Conclusions:
I. Some hard are land.
II. Some stone are hard.
