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GATE 2023 PH – Question 6

General Aptitude · Analytical Aptitude: Logical Reasoning and Deduction · 2 marks · Multiple choice

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.

  1. only (i)
  2. only (iii) and (iv)
  3. only (i) and (ii)
  4. (i), (ii) and (iii)

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Correct answer: (D) (i), (ii) and (iii)

Explanation

Let H = "human beings" and C = "cruel creatures". The statement "Some H are not C" is **false**.

**Step 1: negate it.** The negation of "some H are not C" is "no H is non-cruel", i.e. **all human beings are cruel**.

**Step 2: check each statement.**
- **(i) All human beings are cruel creatures.** This is exactly the negation. ✓
- **(ii) Some human beings are cruel creatures.** Human beings exist in this imagined world (it is said they inhabit it), so if all of them are cruel, at least some are. ✓
- **(iii) Some cruel creatures are human beings.** This is the same statement as (ii) read the other way round. ✓
- **(iv) No human beings are cruel creatures.** This contradicts (i). ✗

Answer: **(i), (ii) and (iii)** (D).