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.
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:
Let's break down Statement II further:
To check if this conclusion follows, we can link the statements together:
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.
To check this conclusion, let's look at the relevant part of Statement II:
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".
Based on our analysis:
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.
Reviewing the process ensures you tackle similar logic problems effectively.
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.
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 forests are hills.
Some hills are deserts.
Conclusions:
(I): All hills are forests.
(II): Some deserts are hills.
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 bottles are ludo.
All ludo are dancer.
Conclusions:
(I): Some dancers are ludo.
(II): All bottles are dancers.