What does $(A\setminus B)$ mean?

Question

This may sound like a stupid question, but what does $(A\setminus B)$ mean in measure theory? I'm asking because the definition of $S$, a a collection of subsets of $[a,b]$, closed under complements of $[a,b]$ is defined as $[a,b]\setminus A \in S$.

Answer 1

In general, $$ A\setminus B $$ is defined as the set of points in $A $ that are not in $ B $. Also, $ B $ need not be a subset of $ A $. If $ B\not\subset A $, then $ A\setminus B=A $.

Answer 2

$A\setminus B= \{x| \,\,x\in A \,\, \wedge \,\,x\notin B\}$