Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. You have to decide which conclusion/s logically follow/s from the given statements. Statement: Some clowns are scary. All scary are ghosts. Some ghosts are friendly. Conclusion (I): All ghosts are friendly. Conclusion (II): All clowns are ghosts.
Neither conclusion (I) nor (II) follow.
Understanding Statements and Conclusions in Logic
This question asks us to analyze given statements and determine which of the provided conclusions logically follow from them. We must treat the statements as true, even if they contradict general knowledge.
Analyzing the Given Statements
We have three statements:
- Statement 1: Some clowns are scary.
- Statement 2: All scary are ghosts.
- Statement 3: Some ghosts are friendly.
These statements describe relationships between four categories: Clowns, Scary, Ghosts, and Friendly. We can visualize these relationships or use logical deduction rules.
Evaluating the Conclusions
Now, let's evaluate each conclusion based on the given statements.
Conclusion (I): All ghosts are friendly.
Statement 3 says, "Some ghosts are friendly." This means there is at least one ghost that is friendly. However, it does not provide information about *all* ghosts. There could be ghosts that are not friendly. Therefore, based on the given statements, we cannot conclude that all ghosts are friendly.
This conclusion does not logically follow from the statements.
Conclusion (II): All clowns are ghosts.
Let's combine Statement 1 and Statement 2:
- Statement 1: Some clowns are scary. (This implies an overlap between the set of Clowns and the set of Scary things).
- Statement 2: All scary are ghosts. (This means the entire set of Scary things is contained within the set of Ghosts).
If some clowns are scary, and all scary things are ghosts, it logically follows that some clowns must be ghosts. This is a standard syllogistic inference (specifically, from "Some A are B" and "All B are C", we can conclude "Some A are C").
However, the conclusion states "All clowns are ghosts". The fact that *some* clowns are ghosts does not mean *all* clowns are ghosts. There might be other clowns who are not scary, and the statements don't tell us if these non-scary clowns are also ghosts. We only know about the clowns who are scary.
Therefore, based on the given statements, we cannot conclude that all clowns are ghosts.
This conclusion does not logically follow from the statements.
Summary of Conclusion Evaluation
| Conclusion | Evaluation | Reasoning |
|---|---|---|
| (I) All ghosts are friendly | Does NOT follow | Statements only say some ghosts are friendly. |
| (II) All clowns are ghosts | Does NOT follow | Statements imply some clowns are ghosts (via scary ones), but not necessarily all clowns. |
Since neither conclusion (I) nor conclusion (II) logically follows from the given statements, the correct option is the one stating that neither conclusion follows.
Revision Table: Key Concepts in Syllogism
| Term | Explanation | Example Logic |
|---|---|---|
| All A are B | Every member of set A is also a member of set B. | A $\subset$ B |
| Some A are B | At least one member of set A is also a member of set B. | A $\cap$ B $\neq \emptyset$ |
| No A are B | No member of set A is a member of set B. | A $\cap$ B $= \emptyset$ |
Additional Information: Types of Logical Statements
The statements used in logic problems like this are often categorized based on their quantity (universal or particular) and quality (affirmative or negative).
- Universal Affirmative (A type): All A are B. (e.g., All scary are ghosts)
- Universal Negative (E type): No A are B. (e.g., No dogs are cats)
- Particular Affirmative (I type): Some A are B. (e.g., Some clowns are scary)
- Particular Negative (O type): Some A are not B. (e.g., Some students are not shy)
Understanding these types helps in systematically analyzing the relationships described in the statements and checking the validity of conclusions.
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.
