Two 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: Some windows are doors. No window is a cupboard. Conclusions: I. No cupboard is a door. II. Some doors are definitely not cupboard.
Only conclusion II follows
Understanding Syllogism and Logical Conclusions
This question tests your ability to draw logical conclusions from given statements. We are provided with two statements about the relationship between windows, doors, and cupboards. We need to determine which of the two conclusions logically follows from these statements, assuming the statements are true.
Analyzing the Statements
Let's break down the given statements:
- Statement 1: Some windows are doors. (Relationship between Windows and Doors)
- Statement 2: No window is a cupboard. (Relationship between Windows and Cupboards)
These statements establish connections between the categories 'Windows', 'Doors', and 'Cupboards'. Statement 1 is a particular affirmative statement (Some A are B), and Statement 2 is a universal negative statement (No A is B).
Visualizing with Venn Diagrams
Venn diagrams are a useful tool to visualize the relationships described in the statements. Let's draw diagrams based on the statements:
- For "Some windows are doors," we draw two overlapping circles, one for 'Windows' and one for 'Doors'. The overlapping region represents the windows that are also doors.
- For "No window is a cupboard," we draw a third circle for 'Cupboards' that does not overlap at all with the 'Windows' circle.
The diagrams would show:
- A region where Windows and Doors overlap.
- A region for Windows that do not overlap with Doors (if any exist according to the statement, but 'Some' doesn't exclude 'All').
- A region for Doors that do not overlap with Windows.
- A region for Cupboards that is completely separate from the Windows circle.
Crucially, the part of the 'Doors' circle that overlaps with the 'Windows' circle *cannot* overlap with the 'Cupboards' circle because the 'Windows' circle and the 'Cupboards' circle are entirely separate.
Evaluating the Conclusions
Now let's evaluate each conclusion based on our understanding from the statements and visualization:
Conclusion I: No cupboard is a door.
This conclusion states that there is no overlap between 'Cupboards' and 'Doors'. Look at the statements again. Statement 1 connects Windows and Doors. Statement 2 connects Windows and Cupboards. There is no direct statement about the relationship between Doors and Cupboards. While Cupboards are separate from Windows, the 'Doors' circle can potentially overlap with the 'Cupboards' circle. The statements do not provide any information that restricts this possibility. Therefore, this conclusion does not necessarily follow.
Conclusion II: Some doors are definitely not cupboard.
This conclusion states that there is at least one part of the 'Doors' category that is separate from the 'Cupboards' category. From Statement 1, we know that "Some windows are doors." This means there is a set of items that are *both* windows *and* doors. Let's call this set 'W & D'. From Statement 2, we know that "No window is a cupboard." This means nothing that is a window can be a cupboard. Since the set 'W & D' consists of items that are windows, none of these items can be cupboards. The set 'W & D' is part of the 'Doors' category (because they are doors). Therefore, the items in the set 'W & D' are doors that are definitely not cupboards. This conclusion logically follows from the statements.
Determining the Following Conclusion(s)
Based on our analysis:
- Conclusion I does not necessarily follow.
- Conclusion II definitely follows.
Therefore, only conclusion II follows from the given statements.
Revision Table: Syllogism Statements and Conclusions
| Statement | Type | Relationship |
|---|---|---|
| Some windows are doors. | Particular Affirmative | Windows & Doors (Overlap) |
| No window is a cupboard. | Universal Negative | Windows & Cupboards (No Overlap) |
| Conclusion | Analysis | Follows? |
|---|---|---|
| I. No cupboard is a door. | Statements don't preclude overlap between Doors and Cupboards. | No |
| II. Some doors are definitely not cupboard. | The doors that are windows cannot be cupboards. | Yes |
Additional Information: Rules of Syllogism
Syllogism problems involve deductive reasoning. Conclusions must be drawn strictly from the given statements, even if they contradict common knowledge. Here are some basic principles:
- If all premises are particular (Some/Some), no universal conclusion (All/No) can be drawn.
- If one premise is particular, the conclusion must be particular.
- If one premise is negative (No/Some...not), the conclusion must be negative.
- No conclusion is possible from two particular premises.
- No conclusion is possible from two negative premises.
- The conclusion cannot be more general than the premises.
In our case, we had one particular affirmative (Some A are B) and one universal negative (No A is C). This combination can sometimes lead to a particular negative conclusion (Some B are not C), which aligns with our finding for Conclusion II ("Some doors are definitely not cupboard.").
Similar Questions
Two 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 teachers are engineers.
All clerks are teachers.
Conclusions:
I. Some engineers are clerks.
II. Some teachers are clerks.
III. Some clerks are not engineers.
Two 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 keys are locks.
All locks are handles.
Conclusions:
I. Some locks are keys.
II. Some handles are keys.
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 switches are fans.
No heater is a fan.
Some wires are heaters.
Conclusions:
I. Some wires are fans.
II. No switch is a heater.
III. No wire is a switch.
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 H are G.
All V are H.
Some V are I.
Conclusions:
I. At least some G are I.
II. All I being H is a possibility.
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 :
Some beds are chairs.
Some chairs are tables.
All tables are cupboards.
Conclusions :
I. Some tables are beds.
II. Some cupboards are chairs.
III. Some cupboards are beds.
Read the given statement(s) 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 statement(s).
Statements :
Some ceilings are beds.
No bed is an apple.
All dogs are beds.
Conclusions :
I. Some ceilings being dogs is a possibility.
II. No dog is an apple.
III. All beds are dogs.
IV. No ceiling is an apple.
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 fans are hammers.
All hammers are fishes.
Conclusions:
I. No fans are fishes.
II. Some fans are fishes.
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 classrooms are schools.
No school is a park.
All houses are parks.
Conclusions:
I. No house is a classroom.
II. No park is a classroom.
III. No school is a house.
Read the given statements and conclusions carefully. Assuming that the information given in the statement 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 fans are coolers.
All coolers are equipment.
Some equipment are mobiles.
Conclusions:
I. Some equipments are fans.
II. Some mobiles are fans.
III. No equipment is fan and cooler both
Two 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 keys are locks.
All locks are handles.
Conclusions:
I. All locks are keys.
II. All handles are keys.
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.
