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Question: use the given sets propositions and set properties to translate...

Question details

Use the given sets, propositions, and set properties to translate the following English-language statements into formal statements. For all formal conditionals, also write the formal contrapositive of the conditional.

1. All writers who understand human nature are clever.

2. No one is a true poet unless he can stir the human heart.

3. Shakespeare wrote Hamlet.

4. No writer who does not understand human nature can stir the human heart.

5. None but a true poet could have written Hamlet.

Sets š‘Š All writers. š‘ƒ All poets.

Propositions š‘ƒ āŠ† š‘Š All poets are writers.Ā Ā š‘†š‘˜ āˆˆ š‘ƒ Shakespeare was a poet.

Set Properties š¶(š‘¤) š‘¤ āˆˆ š‘Š is clever. š»(š‘¤) š‘¤ āˆˆ š‘Š wrote Hamlet. š‘†(š‘¤) š‘¤ āˆˆ š‘Š can stir the human heart. š‘‡(š‘) š‘ āˆˆ š‘ƒ is a true poet. š‘ˆ(š‘¤) š‘¤ āˆˆ š‘Š understands the human heart.

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