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 and decide which conclusion(s) logically follow(s) from the given statements.
Statements:
Some vegetables are fruits.
Some fruits are sweets.
Conclusions:
(I) Some fruits are vegetables.
(II) Some sweets are vegetables.

Question

Prepp Team · Accepted Answer

Analyzing Statements and Conclusions

This question tests our ability to determine logical conclusions based on given statements. We need to assume the statements are true, even if they seem unusual, and then check if the conclusions necessarily follow.

Understanding the Statements

Let's break down the given statements:

Statement 1: All bottles are ludo.
- This means that every single item that is a 'bottle' is also categorized as 'ludo'.
- In terms of sets, the set of 'bottles' is entirely contained within the set of 'ludo'.
Statement 2: All ludo are dancer.
- This means that every single item categorized as 'ludo' is also categorized as a 'dancer'.
- In terms of sets, the set of 'ludo' is entirely contained within the set of 'dancers'.

Evaluating Conclusion (I): Some dancers are ludo.

Let's analyze Conclusion (I) based on Statement 2:

Statement 2 says: "All ludo are dancer."
If all members of the 'ludo' category are also members of the 'dancer' category, it logically follows that at least some members of the 'dancer' category must be 'ludo'.
Think of it this way: If you have a group of ludo, and every one of them is dancing, then the group of dancers must include those ludo. Therefore, some dancers are indeed ludo.
This conclusion logically follows from Statement 2.

Evaluating Conclusion (II): All bottles are dancers.

Now, let's analyze Conclusion (II) using both statements:

From Statement 1, we know: All bottles are ludo.
From Statement 2, we know: All ludo are dancer.
We can link these two statements together. If every bottle is a ludo, and every ludo is a dancer, then it must be true that every bottle is also a dancer.
This follows a transitive property: If A is in B, and B is in C, then A must be in C. In this case, A = bottles, B = ludo, C = dancers.
Therefore, "All bottles are dancers" is a logically valid conclusion.

Final Determination

Based on our analysis:

Conclusion (I): "Some dancers are ludo" logically follows from the statements.
Conclusion (II): "All bottles are dancers" logically follows from the statements.

Since both conclusions logically follow from the given statements, the correct option is the one stating that both conclusions are valid.