Logic 1, WS 2004. Homework 6, given Dec 02, due Dec 09 Prove in informal style, using the basic properties of sets and the inference rules which you consider appropriate:

P(A) = {P |P ⊆ A}

iff

P[∅] = {∅} ∧ ((A¬ = ∅) ⇒ (∀_{a∈A}∀_{P} (P = P(A \ {a}) ⇒ P(A) = P ∪ {B ∪ {a}|B ∈ P }))).