Well i've been having problems trying to prove that $\mathscr{P}(A) \subseteq\mathscr{P}(\mathscr{P}(A)) $ if $ A \subseteq \mathscr{P}(A)$ What i need is to get a proof by using quantifiers
Suppose that $ A \subseteq \mathscr{P}(A)$. Prove $\mathscr{P}(A) \subseteq\mathscr{P}(\mathscr{P}(A)) $
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elementary-set-theory
quantifiers
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4Pick an element of the set on the left. By definition, it is a subset of $A$. By hypothesis, it is a subset of ${\mathcal P}(A)$. By definition, it belongs to the set on the right. Once you follow this, if you really need to "use quantifiers", all you need to do is to write all these statements formally. – 2012-02-29