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{\bf Logic 1, WS 2004.
Homework 6, given Dec 02, due Dec 09}

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\noindent
Prove in informal style, using the basic properties of sets and the inference
rules which you consider appropriate:
$${\cal P}(A) = \{ P | P \subseteq A \}$$
{\centerline {\bf iff}}
$${\cal P}[\emptyset] = \{ \emptyset \}\ \and\ 
((A \neq \emptyset) \impl (\forall_{a \in A} 
   \forall_P (P = {\cal P}(A\setminus\{a\})\ \impl\ 
   {\cal P}(A) = P \cup \{ B \cup \{a\} | B \in P \}))).
$$

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