Question

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 II
• B. Only I and III
• C. Only II and III
• D. Only III

Hint:

To deduce valid inferences, ensure each logical step follows directly from the given statements without assumptions.

Answer 1

The Correct Option is B

Step 1: Understanding the statements. - Statement 1 implies that the set of all heroes is a subset of winners. - Statement 2 implies that the set of all winners is a subset of lucky people. Step 2: Evaluating inferences. - \( I \): All lucky people are heroes. This is incorrect since only some lucky people are heroes. - \( II \): Some lucky people are heroes. This is correct because heroes are a subset of lucky people. - \( III \): Some winners are heroes. This is correct since all heroes are winners. Step 3: Conclusion. The correct answer is \( {(2) Only I and III} \).