In each question below are given three statements followed by two conclusions numbered I and II. You have to take the two/three given statements to be true even if they seem to be at variance from commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts. Statement: Some mobiles are laptops. No laptop is computer. All phones are computer. Conclusion: I. At least some mobiles are computer. II. At least some phone are laptops.
If neither conclusion I nor II follows.
Understanding Statements and Conclusions
This question asks us to evaluate two conclusions based on three given statements. We need to assume the statements are true, even if they contradict common knowledge, and then determine which conclusion logically follows.
Analyzing the Given Statements
Let's break down the statements:
- Statement 1: Some mobiles are laptops. (This indicates an overlap between the set of mobiles and the set of laptops).
- Statement 2: No laptop is computer. (This means the set of laptops and the set of computers are entirely separate).
- Statement 3: All phones are computer. (This means the set of phones is completely contained within the set of computers).
Visualizing with Venn Diagrams
We can represent these relationships using Venn diagrams:
- Draw two overlapping circles for "Mobiles" and "Laptops".
- Draw a third circle for "Computers" completely separate from the "Laptops" circle.
- Draw a fourth circle for "Phones" entirely inside the "Computers" circle.
Evaluating Conclusion I: At least some mobiles are computer.
Let's examine the relationship between "Mobiles" and "Computers".
- We know "Some mobiles are laptops". Let's call the part of mobiles that are laptops 'Mobiles(L)'.
- We know "No laptop is computer". This means 'Mobiles(L)' cannot be computers.
- What about the 'mobiles' that are not 'laptops'? We don't have any information from the statements about whether these mobiles are computers or not. The statements only link mobiles to laptops and laptops to computers.
- Therefore, we cannot definitively conclude that "At least some mobiles are computer" is true. There is no direct or indirect link established between Mobiles and Computers that guarantees an overlap.
Conclusion I does not logically follow from the statements.
Evaluating Conclusion II: At least some phone are laptops.
Let's examine the relationship between "Phones" and "Laptops".
- We know "All phones are computer". This places the entire set of "Phones" inside the "Computers" set.
- We also know "No laptop is computer". This means the entire set of "Laptops" is outside the "Computers" set.
- Since the "Phones" set is inside the "Computers" set, and the "Laptops" set is outside the "Computers" set, the "Phones" set must also be outside the "Laptops" set.
- Therefore, it is impossible for any phone to be a laptop. The conclusion "At least some phone are laptops" is definitely false.
Conclusion II does not logically follow from the statements.
Summary of Conclusions
- Conclusion I: Does not follow.
- Conclusion II: Does not follow.
Based on our analysis, neither conclusion I nor conclusion II follows from the given statements.
Final Answer
The correct option is the one stating that neither conclusion I nor II follows.
Revision Table: Syllogism Rules Quick Check
| Relationship Type | Keywords | Representation | Example |
|---|---|---|---|
| Universal Affirmative | All X are Y | X is subset of Y | All dogs are animals |
| Universal Negative | No X is Y | X and Y are disjoint sets | No dog is a cat |
| Particular Affirmative | Some X are Y | X and Y overlap | Some dogs are brown |
| Particular Negative | Some X are not Y | Part of X is outside Y | Some dogs are not brown |
Additional Information: Types of Syllogism Problems
Statements and conclusion questions, often called syllogisms, are a common type in logical reasoning. They test your ability to derive conclusions from given premises. Key concepts include:
- Statements (Premises): The given sentences that are assumed to be true.
- Conclusions: The sentences that need to be evaluated based on whether they logically follow from the statements.
- Validity: A conclusion is valid if it MUST be true whenever the premises are true. We are only concerned with validity, not real-world truth.
- Possible vs. Definite: A conclusion that is 'possible' is not the same as a conclusion that 'logically follows' (is definite). A conclusion only follows if it is true in ALL possible scenarios based on the statements.
- Negative Statements: Pay close attention to statements with "No" or "not". They create separations between sets.
- "At least some": This phrase is equivalent to "Some". "At least some A are B" means "Some A are B".
Practicing with Venn diagrams or understanding conversion and contraposition rules can help solve these problems efficiently.
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.
Read the given statements and conclusions carefully. Assuming that the information in the statement is true even if they appear to be at variance with commonly known facts, choose the conclusion that logically follows from the statement beyond reasonable doubt.
Statement:-
1. Some dogs are cats.
2. All cats are birds.
Conclusion:-
1. Some dogs are birds.
2. No cat is dog.
