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. Statement I: All hulk are thor. Statement II: All thor are flash. Conclusion I: All hulk are flash. Conclusion II: No thor is a hulk.
Understanding Statements and Conclusions in Logical Reasoning
This question requires us to analyze given statements and determine which of the provided conclusions logically follow from them. We must treat the statements as true, regardless of whether they align with real-world knowledge.
Analyzing the Given Statements
We have two statements:
- Statement I: All hulk are thor.
- Statement II: All thor are flash.
These statements establish relationships between three categories: hulk, thor, and flash. In logical terms, Statement I means the set of 'hulk' is entirely contained within the set of 'thor'. Statement II means the set of 'thor' is entirely contained within the set of 'flash'.
Analyzing the Given Conclusions
We need to evaluate two conclusions:
- Conclusion I: All hulk are flash.
- Conclusion II: No thor is a hulk.
Evaluating Conclusion I: All hulk are flash
Let's consider the relationship described by the statements:
- Statement I says: If something is a hulk, then it is definitely a thor.
- Statement II says: If something is a thor, then it is definitely a flash.
Combining these two statements, if something is a hulk, it must be a thor (from Statement I). And if it is a thor, it must be a flash (from Statement II). Therefore, if something is a hulk, it must logically be a flash.
This can be visualized using simple set inclusion. The set of 'hulk' is inside the set of 'thor', and the set of 'thor' is inside the set of 'flash'. This structure implies that the set of 'hulk' must also be inside the set of 'flash'.
Conclusion I logically follows from the given statements.
Evaluating Conclusion II: No thor is a hulk
Let's look at Statement I again: "All hulk are thor". This means every single hulk is also a thor. This inherently implies that there exist individuals who are both 'hulk' and 'thor' (namely, all the hulks).
Conclusion II states: "No thor is a hulk". This means there is no individual who is both a 'thor' and a 'hulk'.
This directly contradicts Statement I, which tells us that all individuals in the 'hulk' category are also in the 'thor' category. Since Statement I is assumed to be true, Conclusion II must be false.
Conclusion II does not logically follow from the given statements.
Conclusion based on Analysis
Based on our analysis:
- Conclusion I follows from the statements.
- Conclusion II does not follow from the statements.
Therefore, only Conclusion I follows.
| Statement/Conclusion | Analysis | Follows? |
|---|---|---|
| Statement I: All hulk are thor. | Hulk <span>⊆</span> Thor | Given |
| Statement II: All thor are flash. | Thor <span>⊆</span> Flash | Given |
| Conclusion I: All hulk are flash. | If Hulk <span>⊆</span> Thor and Thor <span>⊆</span> Flash, then Hulk <span>⊆</span> Flash. | Yes |
| Conclusion II: No thor is a hulk. | Statement I means some Thor are Hulk (all the ones that are Hulk). Conclusion II says no Thor is Hulk. Contradiction. | No |
Final Answer
Only Conclusion I follows from the given statements.
Revision Table: Logical Reasoning Statements and Conclusions
| Concept | Description | Key takeaway |
|---|---|---|
| Statements | Given propositions assumed to be true for the purpose of the problem. | Treat them as facts, even if they contradict common sense. |
| Conclusions | Propositions derived from the statements. | Must logically follow *only* from the given statements. |
| "All A are B" | Means the set A is a subset of set B. Implies "Some B are A" (if A is not empty). | Does NOT imply "All B are A" or "No A are B". |
| Syllogism | A form of deductive reasoning where a conclusion is drawn from two given or assumed propositions (premises). | The structure "All A are B, All B are C" leading to "All A are C" is a classic valid syllogism. |
Additional Information: Deductive Reasoning and Syllogisms
This problem is an example of deductive reasoning, specifically involving categorical syllogisms. A syllogism is a logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true.
The structure of the valid argument form used for Conclusion I is:
- All P are Q.
- All Q are R.
- Therefore, All P are R.
In our case, P = hulk, Q = thor, and R = flash. Since the statements fit this valid form, the conclusion "All hulk are flash" logically follows.
Understanding these basic structures and how relationships like "All A are B" work is crucial for solving logical reasoning problems. Remember that "All A are B" means every element of A is also an element of B, which necessarily implies that at least some elements of B are also elements of A (specifically, those elements of B that are also elements of A).
Important Questions from Conventional Syllogism
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:
No bank is an office.
All offices are stalls.
Conclusions:
I. No bank is a stall.
II. No stall is a bank.
III. Some stalls are offices.
IV. All the stalls are offices
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 flowers are beautiful.
Vaidehi is beautiful.
Conclusions:
I. Vaidehi is a flower.
II. Some beautiful are flowers.
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:
Some fingers are toes.
Some toes are rings.
Some rings are hands.
Conclusions:
I. Some hands are toes.
II. Some rings are fingers.
III. Some hands are fingers.
V. Some fingers are rings.
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.
