The GATE Grind

GATE 2024 CE (CE2) – Question 2

General Aptitude · Analytical Aptitude: Logical Reasoning and Deduction · 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

Heroes are inside the set of winners, which is inside the set of lucky people. So the converse "all lucky people are heroes" (I) does not follow. Since heroes exist and all of them are winners and lucky, some winners are heroes (III) and some lucky people are heroes (II).