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.
Options:
(A) only (i)
(B) only (iii) and (iv)
(C) only (i) and (ii)
(D) (i), (ii) and (iii)
Official Answer Key:
D
Step-by-Step Solution & Explanation
If "Some human beings are NOT cruel creatures" is FALSE, its negation is TRUE: "All human beings ARE cruel creatures" — this is statement (i). From "All human beings are cruel creatures" (a universal affirmative, assuming the class of human beings is non-empty), it follows by subalternation that "Some human beings are cruel creatures" — statement (ii) — is also true. Also, since all human beings are cruel creatures, human beings form a subset of cruel creatures, so "Some (cruel) creatures are human beings" — statement (iii, by conversion) — is true as well. Statement (iv) directly contradicts (i), so it is false. Answer: (D) (i), (ii) and (iii).
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