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? A. Only I and III B. Only II and III C. Only I and II D. Only III

GATE 2024 · General Aptitude · Statements Follow · medium

Answer: B. Only II and III

1. Build the chain of subsets: Statement 1: Heroes subset Winners. Statement 2: Winners subset Lucky People. Therefore by transitivity: Heroes subset Winners subset Lucky People.
2. Test Inference I: All lucky people are heroes: Inference I claims Lucky People subset Heroes. This is the converse of 'All heroes are lucky'. The converse does not follow. Lucky people can be non-heroes (e.g. a lucky person who is not a winner). Inference I is NOT deducible.
3. Test Inference II: Some lucky people are heroes: Since Heroes subset Lucky People (from step 1), every hero is a lucky person. Assuming at least one hero exists, there is at least one lucky person who is a hero. Therefore Inference II is TRUE.
4. Test Inference III: Some winners are heroes: Since Heroes subset Winners (Statement 1), every hero is a winner. Assuming at least one hero exists, some winners (namely the heroes) are heroes. Therefore Inference III is TRUE.
5. Select the answer: Inferences II and III are deducible; Inference I is not. The answer is B: Only II and III.