Question

In an imagined world: - Some creatures are cruel. - Humans are one kind of creature. - It is given that the statement "Some human beings are not cruel creatures" is FALSE. Which statements 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:

When dealing with quantifiers (some/all/none), remember: if "some are not" is false, then "all are" must be true. This often unlocks the chain of inferences.

Answer 1

The Correct Option is D

Step 1: Interpret the given FALSE statement.
"The statement 'Some human beings are not cruel' is FALSE" means its negation is TRUE: \[ \text{All human beings are cruel}. \] So, (i) is directly true.

Step 2: Check (ii).
If all humans are cruel, then certainly "some humans are cruel" is also true. So (ii) is true.

Step 3: Check (iii).
Since humans are cruel and they are a subset of all creatures, it follows that "some cruel creatures are humans." So (iii) is true.

Step 4: Check (iv).
This contradicts (i). So (iv) is false.

Final Answer:
\[ \boxed{\text{(i), (ii) and (iii)}} \]