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: All chairs are cupboards. Some chairs are radios. No chair is piano. Conclusions: I. Some radios are cupboards. II. Some cupboards are not piano. III. Some radios are not piano.
All of the conclusions follow.
Understanding Syllogism Problems
This type of question tests your ability to draw logical conclusions based on given statements, even if those statements contradict real-world knowledge. We assume the statements are absolutely true and analyze the conclusions based solely on this assumption.
The statements involve relationships between different categories: chairs, cupboards, radios, and pianos. We can visualize these relationships using Venn diagrams, although we will describe the logic here.
Analyzing the Statements
- Statement 1: All chairs are cupboards. This means the set of Chairs is completely contained within the set of Cupboards. If something is a chair, it must also be a cupboard.
- Statement 2: Some chairs are radios. This indicates there is an overlap between the set of Chairs and the set of Radios. There are items that are both chairs and radios. Importantly, this also implies that the set of Chairs is not empty.
- Statement 3: No chair is piano. This means the set of Chairs and the set of Pianos have no overlap. If something is a chair, it cannot be a piano, and vice versa.
Evaluating the Conclusions
Let's examine each conclusion based on the truth of the statements.
Conclusion I: Some radios are cupboards.
We know from Statement 2 that "Some chairs are radios". This means there is at least one item that is both a chair and a radio. Let's consider one such item.
According to Statement 1, "All chairs are cupboards". Since the item we considered is a chair, it must also be a cupboard.
So, we have found an item that is both a radio and a cupboard. This means "Some radios are cupboards".
Therefore, Conclusion I logically follows from the statements.
Conclusion II: Some cupboards are not piano.
From Statement 1, we know "All chairs are cupboards". This implies the existence of chairs (as Statement 2 says "Some chairs are radios", confirming chairs exist). Let's consider any chair.
That chair is a cupboard (from Statement 1).
According to Statement 3, "No chair is piano". Since the item we considered is a chair, it cannot be a piano.
So, we have found an item (a chair) that is a cupboard but is not a piano. This means "Some cupboards are not piano".
Therefore, Conclusion II logically follows from the statements.
Conclusion III: Some radios are not piano.
We know from Statement 2 that "Some chairs are radios". This tells us there are items that are in the intersection of Chairs and Radios. Let's consider one such item. This item is both a chair and a radio.
According to Statement 3, "No chair is piano". Since the item we considered is a chair, it cannot be a piano.
So, we have found an item that is a radio but is not a piano. This means "Some radios are not piano".
Therefore, Conclusion III logically follows from the statements.
Summary of Conclusions
Based on our analysis:
- Conclusion I follows.
- Conclusion II follows.
- Conclusion III follows.
Thus, all of the given conclusions logically follow from the statements.
Revision Table: Statements and Syllogism
| Statement Type | Relationship | Example Syllogism Rule |
|---|---|---|
| All A are B (Universal Affirmative) | Set A ⊂ Set B | If All A are B, and All B are C, then All A are C. |
| Some A are B (Particular Affirmative) | Set A ∩ Set B ≠ ∅ | If Some A are B, and All B are C, then Some A are C. |
| No A is B (Universal Negative) | Set A ∩ Set B = ∅ | If No A is B, and All C are A, then No C is B. |
| Some A are not B (Particular Negative) | Set A \ Set B ≠ ∅ | (Often harder to draw direct conclusions from alone) |
Additional Information: Logical Reasoning Tips
- Always assume the statements are true, even if they seem contradictory to real-world facts.
- Avoid using outside knowledge. Stick strictly to the information given in the statements.
- Use Venn diagrams or set theory notation (\( \forall, \exists, \subset, \cap, \cup, \setminus \)) to visualize the relationships, especially for complex problems.
- Break down complex statements and conclusions into simpler parts.
- Practice with different types of syllogism problems to become familiar with common patterns and fallacies.
Similar Questions
Read the given statements and conclusions carefully. Assuming that the information given in the statements are 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 colours are reds.
2. Some reds are greens.
3. All greens are dark.
Conclusions:
I. All colours being dark is a possibility
II. Some reds are dark.
III. Some reds are colours.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is ture, 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 aero-planes are cars.
All helicopters are cars.
All cars are scooters.
Conclusions:
1. All helicopters are scooters.
2. Some aero-planes are helicopters.
3. No aero-plane is helicopter.
The statements below are followed by two conclusions labelled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow (s) from the information given in the statements.
Statements:
All books are grapes.
Some grapes are fruits.
Conclusions:
I. No grape is a book.
II. Some grapes are books.The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
Some fans are radio.
All fans are light.
Conclusion I: Some radios are light.
Conclusion II: Some lights are radio.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 scissors are spoons.
All spoons are plates.
Conclusions:
1. Some plates are spoons.
2. Some spoons are scissors.
3. Some plates are scissors.
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:
No boat is ship.
Some ships are rods.
Conclusions:
I. No boat is rod.
II. Some rods are ships.
III. Some rods are not boats.
The statements below are followed by two conclusions labelled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
Some tents are cones.
All the cones are motels.
Conclusions:
All the motels are cones.
Some tents are motels.The statements below are followed by four conclusions labelled I, II, III and IV. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
No laptop is notebook.
All notebooks are tablets.
Conclusions:
I. No laptop is tablets.
II. No tablets is laptop.
III. Some tablets are notebooks.
IV. All the tablets are notebooks.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion (s) logically and definitely follow(s) from the information given in the statements.
Statements:
Some cats are hens.
All hens are goat.
Conclusions:
Conclusion I: Some hens are cat.
Conclusion II: Some goats are hens.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 pictures are prizes.
Some prizes are erasers.
Some erasers are helmets.
Conclusions:
I. Some helmets are Prizes.
II. Some erasers are pictures.
III. No helmet is a Prize.
Important Questions from Syllogism
The statements below are followed by conclusions labeled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All twenty are thirty.
All thirty are forty.
All forty are sixty.
All sixty are seventy.
Conclusions:
I. Some forty are thirty.
II. Some seventy are sixty.
III. No thirty is twenty.The statements below are followed by two conclusions labelled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All Strong are animals.
Some animals are Tigers.
All Tigers are Sharp.
Conclusions:
I. Some Strong are Sharp.
II. No Strong is Sharp.The statements below are followed by conclusions labelled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some women are weak.
Some weaks are female.
All female are iron.
All iron are gold.Conclusions:
I. Some weaks are iron.
II. Some gold are weaks.
III. Some women are female.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some teaspoons are glasses.
All teddies are teaspoons.
Conclusions:
I. Some teddies are glasses.
II. Some glasses are teddies.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally Established facts, decide which conclusion(s) logically and definitely follow(s) from the Information, Given in the Statements.
Statements:
All bangles are rings.
Some rings are toys.
Some toys are dolls.
Conclusions:
I. Some rings are bangles.
II. Some dolls are rings.
