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.
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:
- Statement I: All brothers are sisters.
- 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.
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:
All dancers are talented.
Some girls are dancers.
Conclusions:
I. Some girls are talented.
II. All talented are girls.
III. All girls are talented.
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 directors are actors.
No actor is a producer.
All choreographers are directors.
Conclusions:
I. No choreographer is producer.
II. Some actors are choreographers.
III. No director is a producer.
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 follows from the statements.
Statements:
All lemons are plums.
All plums are dates.
Some dates are mangoes.
Conclusions:
I. Some lemons are mangoes.
II. Some mangoes are plums.
III. All lemons are dates.
IV. Some mangoes are dates.
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 cards are postcards.
Some cards are envelopes.
All envelopes are copies.
Conclusions:
I. Some copies are envelopes.
II. Some postcards are copies.
III. Some cards are copies.
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 employees are tax-payers.
Some employees are farmers.
Some farmers are doctors.
Conclusions:
I. No farmer is a tax-payer.
II. Some farmers are tax-payers.
