Question

Statement: All apples are fruits. Some fruits are bananas.
Conclusion I: All apples are bananas.
Conclusion II: Some fruits are not bananas.
Choose the correct option:

• A. Only Conclusion I follows
• B. Neither I nor II follows
• C. Only Conclusion II follows
• D. Both I and II follow

Hint:

In syllogisms, only draw conclusions that are logically necessary based on the given statements. Avoid assumptions beyond what's directly stated.

Answer 1

The Correct Option is C

To resolve this issue, we must examine the provided statements and ascertain which conclusions are logically derivable.

1. Conceptual Framework:

- Premises: Established facts or assertions.
- Inferences: Deductions made from the premises.
- Employ logical reasoning and set theory principles for assessment.

2. Provided Premises:

- Every apple is a fruit.
- A subset of fruits are bananas.

3. Assessment of Inferences:

- Inference I: All apples are bananas.
Given that all apples are fruits, and only a portion of fruits are bananas, it cannot be concluded that all apples are bananas. Thus, Inference I is invalid.

- Inference II: Some fruits are not bananas.
Since a portion of fruits are bananas, the remaining fruits are by definition not bananas. Therefore, Inference II is valid.

Conclusion:

Only Inference II is valid, indicating that option C is the correct choice.