Q.6 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)
The statement “Some human beings are not cruel creatures” being FALSE implies that all human beings are cruel creatures, as this is the logical negation in categorical terms (no human beings lack the property of being cruel).
Logical Analysis
In syllogistic logic, the statement “Some H are not C” (H = human beings, C = cruel creatures) is false only when the entire class H is included in C, meaning “All H are C.” The given premise “some creatures are cruel” ensures the universe allows cruelty but doesn’t alter this negation. Thus, (i) “All human beings are cruel creatures” follows with certainty.
Option Breakdown
-
(i): True, as the direct negation.
-
(ii) “Some human beings are cruel creatures”: Does not follow with certainty; “all” implies “some,” but certainty requires testing all cases—here, “all” is certain, so “some” is too (since all includes some).
-
(iii) “Some creatures that are cruel are human beings”: Equivalent to (ii); follows from “all humans are cruel” overlapping with “some cruel creatures.”
-
(iv) “No human beings are cruel creatures”: Directly contradicts (i); cannot follow.
Options (A) only (i) misses (ii)/(iii); (B) includes false (iv); (C) only (i)/(ii) misses (iii). Correct: (D) (i), (ii), and (iii).
Human beings are one among many creatures that inhabit an imagined world where some creatures are cruel—this GATE 2023 logical inference question tests negation in categorical syllogisms. When “some human beings are not cruel creatures” is FALSE, what follows with certainty? Explore logical inference “some human beings are not cruel creatures” false for IIT JAM/GATE prep.
Core Logic Negation
The particular negative “Some H are not C” falsifies only under universal affirmative “All H are C.” No partial overlap works; all humans must be cruel creatures. This aligns with Aristotelian logic rules.
GATE Options Explained
| Option | Statement | Follows? | Reason |
|---|---|---|---|
| (i) | All human beings are cruel creatures | Yes | Direct negation of “some not.” |
| (ii) | Some human beings are cruel creatures | Yes | “All” entails “some.” |
| (iii) | Some cruel creatures are human beings | Yes | Symmetric to (ii); overlaps with “some creatures cruel.” |
| (iv) | No human beings are cruel creatures | No | Contradicts (i). |
Answer: D.
Exam Tips
Practice negations: “Some not P” false → “All P.” Use Venn diagrams—H circle fully inside C. Common trap: Assuming “some” without “all” certainty.
