Example Question #1 : Logical Conclusions Given Two True Statements
1. All writers live in fear of a lonely, penniless death.
2. I live in fear of a lonely, penniless death.
3. I am a writer.
If the first two statements are true, is the third statement true, false, or uncertain?
There is not enough information given to say if the third statement is true. The relationship between the two sentences is only directly true in one direction, namely that all writers live in fear of a lonely penniless death. It does NOT hold that all people who live in fear of a penniless death are, by definition, writers. It is possible that the speaker is a writer, but the logic of the statement's does not necessitate that this is so.
Example Question #2 : Logical Conclusions Given Two True Statements
All ducks like oranges.
Fluffy does not like oranges.
Is Fluffy a duck?
Suppose Fluffy is a duck. Then by the first statement, Fluffy must like oranges. But by the second statement, Fluffy hates oranges, so this would be a contradiction. Therefore, Fluffy cannot be a duck.