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## Main Question or Discussion Point

I'm trying to proof an identity from Munkres' Topology

A \ ( A \ B ) = B

By definition A \ B = {x : x in A and x not in B}

A \( A \ B) = A \ (A ∩ B

What did I miss?

A \ ( A \ B ) = B

By definition A \ B = {x : x in A and x not in B}

A \( A \ B) = A \ (A ∩ B

^{c}) = A ∩ (A ∩ B^{c})^{c}= A ∩ (A^{c}∪ B) = (A ∩ A^{c}) ∪ (A ∩ B) = ∅ ∪ (A ∩ B) = A ∩ BWhat did I miss?