Discussion
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?
Answer: B
The valid inferences are Only II and III.
From 'all heroes are winners' and 'all winners are lucky', every hero is lucky. So, assuming heroes exist as the usual reading of such statements does, some lucky people are heroes (II), and some winners are heroes (III), the converse of statement 1 limited to 'some'.
I does not follow: the lucky people may include many who are not heroes, so 'all lucky people are heroes' reverses the inclusion. Every option containing I is therefore wrong, and 'Only III' leaves out II, which follows just as directly.
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