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:

- Always negate carefully: If “Some X are not Y” is FALSE, then it means “All X are Y.”
- From universal truths (“all”), you can always infer particular truths (“some”).
- Eliminate contradictions systematically.

Answer 1

The Correct Option is D

Step 1: The statement “Some human beings are not cruel creatures” is given as FALSE.
\(\Rightarrow\) This means the opposite is TRUE: “No human beings are not cruel.”
\(\Rightarrow\) All human beings must be cruel creatures.
Step 2: If all human beings are cruel, then naturally:
- (i) All human beings are cruel creatures \(\Rightarrow\) TRUE.
Step 3: If all human beings are cruel, then certainly some of them are cruel.
- (ii) Some human beings are cruel creatures \(\Rightarrow\) TRUE.
Step 4: Since humans are part of the set of cruel creatures, some creatures that are cruel are indeed human beings.
- (iii) Some creatures that are cruel are human beings \(\Rightarrow\) TRUE.
Step 5: Statement (iv) says no human beings are cruel creatures. This contradicts the result from Step 1, so it is FALSE.
Final Conclusion: The statements (i), (ii), and (iii) can be logically inferred with certainty.
\[\boxed{\text{Correct Answer: (D)}}\]