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?
 

Thread 'Two interesting number theory tricks'

First trick I learned this one a long time ago and have used it to entertain and amuse young kids. Ask your friend to write down a three-digit number without showing it to you. Then ask him or her to rearrange the digits to form a new three-digit number. After that, write whichever is the larger number above the other number, and then subtract the smaller from the larger, making sure that you don't see any of the numbers. Then ask the young "victim" to tell you any two of the digits of the...
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