In the question three statements are given, followed by two conclusions, I and II. You have to consider the statements to be true even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements. Statements: I. Some walls are broken. II. All windows are broken. III. Some walls are not painted. Conclusions: I. Some broken are windows. II. All windows are painted.
Understanding Logic Statements and Conclusions
This question asks us to analyze three statements and determine which of the two given conclusions logically follows from them. We must treat the statements as true, even if they contradict common knowledge.
Analyzing the Statements
Let's break down the given statements:
- Statement I: Some walls are broken. This indicates a partial overlap between the set of 'Walls' and the set of 'Broken' things.
- Statement II: All windows are broken. This is a strong statement. It means that the set of 'Windows' is completely contained within the set of 'Broken' things. If something is a window, it must also be broken.
- Statement III: Some walls are not painted. This indicates a partial separation between the set of 'Walls' and the set of 'Painted' things. There's a portion of walls that falls outside the set of painted things.
Analyzing the Conclusions
Now, let's evaluate each conclusion based on the statements:
Conclusion I: Some broken are windows.
- Consider Statement II: "All windows are broken".
- If all members of one group (windows) are part of another group (broken), it necessarily means that some members of the larger group (broken) must be from the smaller group (windows).
- Think of it this way: If every single window is in the set of broken items, then the set of broken items definitely includes all the windows. Therefore, some of the items in the 'broken' category are indeed 'windows'.
- This conclusion logically follows directly from Statement II.
Conclusion II: All windows are painted.
- We need to find a connection between 'Windows' and 'Painted' based on the statements.
- Statement II links 'Windows' to 'Broken'.
- Statements I and III link 'Walls' to 'Broken' and 'Painted'.
- Statement I: Some walls are broken.
- Statement III: Some walls are not painted.
- There is no statement that directly relates 'Windows' to 'Painted'. The information about 'Walls' being broken or not painted does not provide any logical bridge to determine if 'Windows' are painted. Just because windows are broken (like some walls) and some walls are not painted, doesn't tell us anything about the paint status of windows.
- This conclusion does not logically follow from the given statements.
Determining Which Conclusion(s) Follow
Based on our analysis:
- Conclusion I (Some broken are windows) follows from Statement II.
- Conclusion II (All windows are painted) does not follow from any combination of the statements.
Therefore, only conclusion I follows from the given statements.
Revision Table: Key Concepts in Syllogism
| Concept | Explanation | Example (from statements) |
|---|---|---|
| All A are B | The set A is completely inside the set B. Implies Some B are A. | All windows are broken (Statement II) |
| Some A are B | There is at least one element common to sets A and B. | Some walls are broken (Statement I) |
| Some A are not B | There is at least one element in set A that is not in set B. | Some walls are not painted (Statement III) |
| No A are B | Set A and Set B have no elements in common. (Not used in this problem) | - |
Additional Information: Venn Diagrams for Syllogism
Syllogism problems can often be visualized using Venn diagrams. Each category (Walls, Broken, Windows, Painted) can be represented by a circle. The relationships described in the statements determine how these circles overlap or are separated.
- "All windows are broken" means the 'Windows' circle is drawn completely inside the 'Broken' circle.
- "Some walls are broken" means the 'Walls' and 'Broken' circles overlap.
- "Some walls are not painted" means a part of the 'Walls' circle is outside the 'Painted' circle.
Drawing these diagrams can help confirm the logical flow. For Conclusion I ("Some broken are windows"), seeing the 'Windows' circle inside the 'Broken' circle clearly shows that the overlapping area is the 'Windows' circle itself, confirming that some (in fact, all) windows are broken, and thus some broken things are windows. For Conclusion II ("All windows are painted"), you would find no direct or indirect connection established by the statements that places the 'Windows' circle entirely inside the 'Painted' circle or even partially inside it in a definitive way.
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.
