Question

Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world, it is given that the statement "Some human beings are not cruel creatures" is FALSE, then which of the following set of statement(s) can be logically inferred with certainty?
(i) All human beings are cruel creatures.
(ii) Some human beings are cruel creatures.
(iii) Some creatures that are cruel are human beings.
(iv) No human beings are cruel creatures.

• A. only (i)
• B. only (iii) and (iv)
• C. only (i) and (ii)
• D. (i), (ii) and (iii)

Hint:

- Logical inferences depend on the truth or falsity of the given premises.
- If a premise is negated, its opposite becomes a valid inference.
- In this case, the negation of "Some human beings are not cruel" leads to the conclusion that all human beings are cruel.

Answer 1

The Correct Option is C

Step 1: Understand the Given Premise
We are given that in this imagined world, it is stated that "Some human beings are not cruel creatures" is FALSE. This implies that the opposite must be true: every human being is a cruel creature. This is a critical point to understanding the logical implications.
Thus, based on the falsity of the statement "Some human beings are not cruel creatures," we can confidently infer that:
- Every human being must be a cruel creature.
Step 2: Analyze the Statements
We are asked which of the following statements can be logically inferred with certainty based on the given premise.
(i) All human beings are cruel creatures.
- This is a direct consequence of the given premise. Since the statement "Some human beings are not cruel creatures" is false, we can infer that all human beings are indeed cruel. Hence, statement (i) is true.
(ii) Some human beings are cruel creatures.
- This statement is also true because we have already established that all human beings are cruel creatures. Therefore, the statement "Some human beings are cruel creatures" is certainly true, as all human beings are cruel by definition.
(iii) Some creatures that are cruel are human beings.
- This statement does not necessarily follow from the given information. It is possible that all cruel creatures in the imagined world are human beings, but the statement does not logically follow with certainty based on the given premise.
(iv) No human beings are cruel creatures.
- This statement contradicts the premise that all human beings are cruel creatures. Hence, this statement is false. Step 3: Conclusion
Based on the analysis, the only statements that can be logically inferred with certainty are (i) and (ii).
The correct answer is (C).