MHB Identity Proof: (A-B)-C=A-(B∪C)

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To prove the identity (A-B)-C=A-(B∪C), the discussion highlights the use of set identities, specifically A-B=A\bar{B} and \overline{B∪C}=\bar{B}\bar{C}. The proof involves manipulating these identities to show the equivalence. The conversation emphasizes the importance of understanding set operations and their properties, including commutativity and associativity. Participants are encouraged to apply the provided identities to validate the equality. This exploration of set theory identities is crucial for grasping advanced concepts in mathematics.
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Show that(A-B)-C=A-(BUC)
 
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This can be shown using identities on sets. Two identities are: $A-B=A\bar{B}$ and $\overline{B\cup C}=\bar{B}\bar{C}$. Here $\bar{A}$ denotes the complement of $A$, and I skip intersection, i.e., I write $AB$ for $A\cap B$. There are numerous other identities on sets, such as commutativity and associativity of intersection and union, laws involving the empty set and so on. Can you use the ones I provided to prove your equality?
 

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