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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?
- Only I and II
- Only II and III
- Only I and III
- Only III
Correct answer: Only III
Solution
From the statements, heroes are a subset of winners, and winners are a subset of lucky people. Therefore, heroes are also winners, so some winners are heroes if heroes exist; in standard syllogism interpretation, this is the valid conclusion among the options. The reverse statements I and II do not follow because the set inclusion cannot be reversed.
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