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Question

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.

Statement I: All brothers are sisters.

Statement II: All sisters are wives and all wives are sons.

Conclusion I: All brothers are sons.

Conclusion II: Some sons are wives.

The correct answer is Both conclusions I and II follows.

Let's carefully analyze the given statements and conclusions to determine which logically follow.

Understanding the Statements in Logic Problems

In logic questions like this, we must assume the statements are absolutely true, even if they contradict real-world knowledge. We need to build a logical connection based only on the provided information.

We have two statements:

  1. Statement I: All brothers are sisters.
  2. Statement II: All sisters are wives and all wives are sons.

Let's break down Statement II further:

  • All sisters are wives.
  • All wives are sons.

Analyzing Conclusion I: All brothers are sons

To check if this conclusion follows, we can link the statements together:

  • From Statement I, we know that if someone is a brother, they are a sister. We can represent this as: Brothers $\rightarrow$ Sisters.
  • From Statement II, we know that if someone is a sister, they are a wife. We can represent this as: Sisters $\rightarrow$ Wives.
  • Also from Statement II, we know that if someone is a wife, they are a son. We can represent this as: Wives $\rightarrow$ Sons.

We can chain these relationships together:

Brothers $\rightarrow$ Sisters $\rightarrow$ Wives $\rightarrow$ Sons

This chain logically implies that if someone is a brother, they must also be a son.

Therefore, the conclusion "All brothers are sons" logically follows from the given statements.

Analyzing Conclusion II: Some sons are wives

To check this conclusion, let's look at the relevant part of Statement II:

  • All wives are sons.

This statement means that the set of 'Wives' is entirely contained within the set of 'Sons'. If all members of set A are members of set B, then it is necessarily true that some members of set B are members of set A (specifically, those members of B that are also members of A, which are all of A in this case). In simple terms, if every single wife is also a son, then there must be at least some sons who are wives (in fact, all wives are sons).

Therefore, the conclusion "Some sons are wives" logically follows from the statement "All wives are sons".

Synthesizing the Findings for Logical Reasoning

Based on our analysis:

  • Conclusion I (All brothers are sons) follows.
  • Conclusion II (Some sons are wives) follows.

Thus, both conclusions logically follow from the given statements.

Statement/Conclusion Logical Representation Follows? Reasoning
Statement I All Brothers are Sisters (B $\rightarrow$ S) Given as True Base premise
Statement II (part 1) All Sisters are Wives (S $\rightarrow$ W) Given as True Base premise
Statement II (part 2) All Wives are Sons (W $\rightarrow$ Z) Given as True Base premise
Conclusion I All Brothers are Sons (B $\rightarrow$ Z) Yes Chain: B $\rightarrow$ S $\rightarrow$ W $\rightarrow$ Z
Conclusion II Some Sons are Wives (Some Z are W) Yes If All W are Z, then Some Z are W

The correct option is the one stating that both conclusions I and II follow.

Revision Table: Checking Logic Statements and Conclusions

Reviewing the process ensures you tackle similar logic problems effectively.

  • Identify the categories mentioned (Brothers, Sisters, Wives, Sons).
  • Translate statements into simple logical relationships (e.g., "All X are Y" means X $\rightarrow$ Y or X is a subset of Y).
  • Chain the relationships together to test "All" conclusions.
  • Remember that "All A are B" implies "Some B are A".
  • Evaluate each conclusion against the combined information from the statements.

Additional Information: Types of Logical Inferences

This problem involves deductive reasoning, specifically dealing with categorical syllogisms and immediate inferences. The rule "All A are B" implies "Some B are A" is an example of an immediate inference called conversion by limitation (though modern logic often simplifies it by noting 'Some' doesn't imply existence, but follows from the universal premise). The chaining of "All A are B" and "All B are C" to conclude "All A are C" is a fundamental principle of syllogistic reasoning, known as transitivity.

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Important Questions from Syllogism

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

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