Question: use the given sets propositions and set properties to translate...
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 𝑊 All writers. 𝑃 All poets.
Propositions 𝑃 ⊆ 𝑊 All poets are writers. 𝑆𝑘 ∈ 𝑃 Shakespeare was a poet.
Set Properties 𝐶(𝑤) 𝑤 ∈ 𝑊 is clever. 𝐻(𝑤) 𝑤 ∈ 𝑊 wrote Hamlet. 𝑆(𝑤) 𝑤 ∈ 𝑊 can stir the human heart. 𝑇(𝑝) 𝑝 ∈ 𝑃 is a true poet. 𝑈(𝑤) 𝑤 ∈ 𝑊 understands the human heart.