Prove $(A^c)^c$ = $A$
$(A^c)^c = \{x|x\in (A^c)^c\}$
$(A^c)^c = \{x|x\notin A^c\}$ by definition of complement
$(A^c)^c = \{x|\ (x \in A)\}$ by definition of complement
Therefore
$(A^c)^c=A$
Is this proof ok, I'm not sure if its valid? thanks
Prove $(A^c)^c$ = $A$
$(A^c)^c = \{x|x\in (A^c)^c\}$
$(A^c)^c = \{x|x\notin A^c\}$ by definition of complement
$(A^c)^c = \{x|\ (x \in A)\}$ by definition of complement
Therefore
$(A^c)^c=A$
Is this proof ok, I'm not sure if its valid? thanks
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