Definition 3.1.27 (Difference sets). Given two sets \(A\) and \(B\), we define the set \(A-B\) or \(A\setminus B\) to be the set \(A\) with any elements of \(B\) removed: $$ A\setminus B:=\{x\in A:x\notin B\}; $$ for instance, \(\{1,2,3,4\}\setminus\{2,4,6\}=\{1,3\}\). In many cases \(B\) will be a subset of \(A\), but not necessarily.
Definition 3.1.27
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Exercise 3.4.3
\(\equiv\) { Definition 3.1.27 }