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GATE 2024 MN – Question 2

General Aptitude · Analytical Aptitude: Logical Reasoning, Deduction and Analogy · 1 mark · Multiple choice

Statements:
1. All heroes are winners.
2. All winners are lucky people.
Inferences:
I. All lucky people are heroes.
II. Some lucky people are heroes.
III. Some winners are heroes.

Which of the above inferences can be logically deduced from statements 1 and 2?

  1. Only I and II
  2. Only II and III
  3. Only I and III
  4. Only III

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Correct answer: (B) Only II and III

Explanation

The premises give heroes⊆winners⊆lucky people. In the conventional syllogism interpretation that heroes exist, choose a hero: that person is both a winner and lucky. This proves II and III.

I reverses the containment and need not hold. For example, let one person be a hero, winner and lucky, and another be lucky only. Both premises remain true but not every lucky person is a hero.

The keyed answer is **B, II and III**. In modern predicate logic, universal statements alone do not assert that heroes exist; if that set were empty, neither existential conclusion would be guaranteed. The existence convention is needed for the intended answer.

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