I have a task to calculate a double integral on a region $D=A\setminus B$, where $A=\{(x,y): \text{some system of inequalities}\}, B= \{(x,y): \text{another system of inequalities}\}$. What does operator "$\setminus$" mean?
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$\begingroup$"$\,A\setminus B\;$" $\,$ means the $A$ "set minus" $B$: that is, it defines a region which contains all points $(x, y)$ such that $\,(x, y) \in A,\,$ but $\,(x, y) \notin B$.
$$A\setminus B = \{ (x, y)\mid (x, y) \in A \land (x, y) \notin B\}.$$
In your case, the region $A\setminus B$ means "all points satisfying the system of inequalities defining set $A$, but not satisfying the system of inequalities defining set $B$.
$\endgroup$ $\begingroup$This is the set difference operator. $A\setminus B=\{a\in A\mid a\notin B\}$.
For example $\{0,1\}\setminus\{1\}=\{0\}$. And $\Bbb Z\setminus\Bbb N$ is the set of negative numbers. $\Bbb R\setminus\Bbb Q$ is the set of irrational numbers, and so on.
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