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. Some tables are chairs. 2. Some chairs are beds. 3. All beds are goods. Conclusions: I. Some chairs are goods. Il. Some goods are not beds.
Only conclusion I follows
Understanding Syllogism Statements and Conclusions
This question asks us to analyze given statements and determine which conclusions logically follow. We must treat the statements as true, regardless of whether they align with real-world facts. This type of problem tests our ability to apply deductive reasoning based on the provided information.
Analyzing the Statements:
Let's represent the categories involved:
- Tables (T)
- Chairs (C)
- Beds (B)
- Goods (G)
The statements are:
- Some tables are chairs. (Some T are C)
- Some chairs are beds. (Some C are B)
- All beds are goods. (All B are G)
These statements describe relationships between these categories. "Some" implies that there is at least one element common to both categories, but not necessarily all. "All" implies that every element of the first category is included in the second category.
Analyzing the Conclusions:
We need to check if the following conclusions logically follow from the statements:
- Conclusion I: Some chairs are goods. (Some C are G)
- Conclusion II: Some goods are not beds. (Some G are not B)
Evaluating Conclusion I: Some chairs are goods.
Let's look at the statements involving Chairs (C) and Goods (G):
- Statement 2: Some chairs are beds. (Some C are B)
- Statement 3: All beds are goods. (All B are G)
Statement 2 tells us there is an overlap between Chairs and Beds. Statement 3 tells us that everything that is a Bed is also a Good. If some Chairs are Beds, and all Beds are Goods, then those Chairs that are Beds must also be Goods. Therefore, there must be an overlap between Chairs and Goods.
Consider a simple example: If some of your friends are students, and all students like to read, then those friends who are students must also like to read. So, some of your friends like to read.
Similarly, since Some chairs are beds and All beds are goods, it logically follows that Some chairs are goods.
Conclusion I logically follows.
Evaluating Conclusion II: Some goods are not beds.
Let's look at the statement involving Goods (G) and Beds (B):
- Statement 3: All beds are goods. (All B are G)
This statement means that the set of Beds is entirely contained within the set of Goods. This can be visualized as a smaller circle (Beds) completely inside a larger circle (Goods). However, this statement does not tell us anything about whether there are any Goods that are *not* Beds.
Consider two possibilities for Statement 3 (All B are G) to be true:
- The set of Beds is a proper subset of the set of Goods (i.e., there are Goods that are not Beds). In this case, "Some goods are not beds" would be true.
- The set of Beds is exactly the same as the set of Goods (i.e., All Beds are Goods, AND All Goods are Beds). In this case, there are no Goods that are not Beds, so "Some goods are not beds" would be false.
Since Statement 3 allows for the possibility that Beds and Goods are the same set, we cannot definitively conclude that "Some goods are not beds" is always true based *only* on the given statements. A conclusion must logically follow in all possible scenarios where the statements are true.
Conclusion II does not logically follow.
Summary of Conclusions:
- Conclusion I: Some chairs are goods - Follows
- Conclusion II: Some goods are not beds - Does Not Follow
Therefore, only conclusion I follows from the given statements.
Revision Table: Syllogism Rules
| Statement Type | Relationship | Example |
|---|---|---|
| All A are B | A is a subset of B | All dogs are mammals |
| No A are B | A and B are disjoint sets | No cats are dogs |
| Some A are B | A and B overlap | Some students are athletes |
| Some A are not B | A and the complement of B overlap | Some students are not athletes |
Additional Information: Deductive Reasoning
Syllogism problems are a form of deductive reasoning. Deductive reasoning starts with general statements (premises) and reaches a specific conclusion that is logically certain if the premises are true. Unlike inductive reasoning (which moves from specific observations to general conclusions), deductive reasoning guarantees the truth of the conclusion if the premises are true and the logic is valid.
Key points about deductive reasoning:
- If the premises are true and the argument form is valid, the conclusion must be true.
- Syllogisms typically involve two premises and one conclusion.
- Common methods for evaluating syllogisms include Venn diagrams or logical rules (though advanced rules were not strictly needed for this specific problem).
- We must strictly adhere to the information given in the statements and not bring in outside knowledge.
Similar Questions
- All flowers are plants. Some plants are flowering plants. Which conclusion is logically valid?
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 f act s, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some carpenters are singers.
All singers are doctors.
Conclusions:
I. No doctor is a carpenter.
II. Some doctors are singers.
III. Some carpenters are doctors.
Three statements are given, followed by three conclusions numbered I, II and III. Assuming the statement s 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 machines are coolers.
All coolers are robots.
Some microwaves are coolers.
Conclusions:
I. Some coolers are machines.
II. Some robots are machines.
III. No robot is a microwave.
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:
1. All teachers are students.
2. All principal are teachers.
3. Some principals are doctors.
Conclusions:
I. Some students are teachers.
II. No student is a doctor.
III. Some students are principals.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:
1. All apples are mangoes.
2. Some bananas are mangoes.
Conclusions:
I. Some mangoes are bananas.
II. Some mangoes are apples.
III. No mango is an apple.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:
1. No bed is a chair.
2. All tables are beds.
3. No cupboard is a bed.
Conclusions:
I. No table is a chair.
II. No cupboard is a table.
III. Some beds are tables.
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. No city is a district.
2. Some districts are zones.
3. Some zones are states.
Conclusions:
I. Some zones are districts.
II. Some districts are cities.
lII. No state is a zone.
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:
No man is engineer.
No engineer is driver.
Some drivers are shop-keepers.
Conclusions:
1. Some men are drivers.
2. No shop-keepers are engineer.
3. Some shop-keepers are not engineers.
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.
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 pillows are doors.
Some doors are beds.
Conclusions:
I. Some doors are pillows.
II. All beds are doors.
Important Questions from 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:
Some students are players.
All players are male.
Conclusions:
I. All males are players.
II. Some males are students.
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 creative is an employer.
All experts are creative.
All workers are experts.
Conclusions:
I. No employer is an expert.
II. No worker is an employer.
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 actors are choreographers.
All choreographers are producers.
Not a single producer is a director.
Conclusions:
I. Some actors are directors.
II. Not a single actor is a director.
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 flowers are tulips.
2. No tulips are whites.
Conclusions :
I. All tulips are flowers.
II. Some tulips are whites.
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 rats are dogs.
Some rats are hens.
Conclusions:
I. Some rats are dogs.
II. Some hens are rats.
