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 and definitely follow/s from the given statements. Statements: All Shoes are Feet. Some Shoes are Boxes. All Boxes are Houses. Conclusions: (I) Some Houses are Shoes. (II) Some Feet are Boxes.
Both conclusions (I) and (II) follow.
Understanding Syllogism and Logical Conclusions
This question tests our ability to interpret given statements and determine which conclusions logically follow. In syllogism, the statements are assumed to be true, even if they contradict common knowledge. We need to apply rules of logic or use visual aids like Venn diagrams to arrive at the correct conclusions.
Analyzing the Given Statements
We are given the following statements:
- Statement 1: All Shoes are Feet.
- Statement 2: Some Shoes are Boxes.
- Statement 3: All Boxes are Houses.
Analyzing the Conclusions
We need to check if the following conclusions logically follow from the statements:
- Conclusion (I): Some Houses are Shoes.
- Conclusion (II): Some Feet are Boxes.
Step-by-Step Verification using Logical Deduction
Let's analyze each conclusion based on the provided statements.
Verification of Conclusion (I): Some Houses are Shoes.
We have the statements:
- Statement 2: Some Shoes are Boxes.
- Statement 3: All Boxes are Houses.
From "Some Shoes are Boxes" and "All Boxes are Houses", we can logically deduce a connection between Shoes and Houses. If there are some Shoes that are Boxes, and every single Box is a House, then those specific Shoes (which are also Boxes) must also be Houses.
This inference follows a pattern: Some A are B, All B are C ∴ Some A are C.
Here, A = Shoes, B = Boxes, C = Houses.
So, Some Shoes are Boxes, and All Boxes are Houses ∴ Some Shoes are Houses.
If Some Shoes are Houses, then it logically follows that Some Houses are Shoes (this is a simple conversion rule for 'I' type statements - Some A are B is equivalent to Some B are A).
Therefore, Conclusion (I) Some Houses are Shoes logically follows from the given statements.
Verification of Conclusion (II): Some Feet are Boxes.
We have the statements:
- Statement 1: All Shoes are Feet.
- Statement 2: Some Shoes are Boxes.
From "Some Shoes are Boxes" and "All Shoes are Feet", we can deduce a relationship between Feet and Boxes. Statement 2 tells us there is an overlap between Shoes and Boxes. Statement 1 tells us that the entire set of Shoes is contained within the set of Feet. Therefore, the overlap area between Shoes and Boxes must necessarily be inside the set of Feet.
This means that the things that are both Shoes and Boxes are also Feet. So, there are some Feet that are Boxes.
This inference follows a pattern: All A are B, Some A are C ∴ Some B are C.
Here, A = Shoes, B = Feet, C = Boxes.
So, All Shoes are Feet, and Some Shoes are Boxes ∴ Some Feet are Boxes.
Therefore, Conclusion (II) Some Feet are Boxes logically follows from the given statements.
Summary of Conclusions
Based on our analysis:
- Conclusion (I) Some Houses are Shoes: Follows.
- Conclusion (II) Some Feet are Boxes: Follows.
Both conclusions logically follow from the given statements.
| Statement | Type |
|---|---|
| All Shoes are Feet | Universal Affirmative (A) |
| Some Shoes are Boxes | Particular Affirmative (I) |
| All Boxes are Houses | Universal Affirmative (A) |
| Conclusion | Follows? | Reasoning |
|---|---|---|
| (I) Some Houses are Shoes | Yes | Some Shoes are Boxes (I) + All Boxes are Houses (A) ∴ Some Shoes are Houses (I). Conversion of Some Shoes are Houses (I) is Some Houses are Shoes (I). |
| (II) Some Feet are Boxes | Yes | All Shoes are Feet (A) + Some Shoes are Boxes (I) ∴ Some Feet are Boxes (I). |
Revision Table: Syllogism Basics
Understanding the types of statements is crucial for solving syllogism problems.
| Type | Statement Structure | Example | Quantifier |
|---|---|---|---|
| A (Universal Affirmative) | All S are P | All cats are mammals | All, Every |
| E (Universal Negative) | No S are P | No dogs are birds | No, None |
| I (Particular Affirmative) | Some S are P | Some students are athletes | Some, Few, Most, Many |
| O (Particular Negative) | Some S are not P | Some birds are not black | Some... not |
Additional Information: Solving Syllogisms
Syllogism problems can be solved using various methods, including:
- Venn Diagrams: This is a visual method where circles represent categories. Overlapping or enclosed circles show the relationships between them. You draw diagrams for the statements and then check if the conclusion is always represented in the diagram.
- Rules of Syllogism: There are formal rules regarding the distribution of terms, the quality and quantity of statements, and the valid combinations of premises that lead to necessary conclusions. Understanding these rules allows for a more formal deduction process.
- Table Method: Creating a table to track the relationships (like 'All', 'Some', 'No') between the terms based on the statements.
For this question, both Venn diagrams and logical deduction based on statement types confirm that both conclusions follow.
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.
