Let $E, F$ be two sets.
1) If $E$ is empty and $F$ is nonempty, is their difference $E \setminus F$ meaningful?
2) If $E, F$ are both nonempty and disjoint, is their difference $E \setminus F$ meaningful?
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$\begingroup$Yes to both questions.
Recall that $E\setminus F=\{x\in E\mid x\notin F\}$. In both cases the answer is fairly easy to calculate, and I'll leave it for you to do so.
The point is that there is meaning as long as $E$ and $F$ are sets. And the empty set is a set (proof by terminology).
$\endgroup$ 3 $\begingroup$Hint: If you think of forming $E\setminus F$ as "start with everything that's in $E$, then remove everything that's also in $F$", you should be able to answer both of these questions easily.
$\endgroup$ $\begingroup$To aid the above answers with some intuition, think of $E \backslash F$ as the set $E$ "without" elements of $F$, i.e. $E \cap F^c$, the set of all elements of $E$ that are not in $F$.
So, as for the first, let $E$ be the set of United States presidents prior to the current date that were female. Then $E$ is (shamefully) empty. Let $F$ be the set of all red-headed humans, past and present. What, then, are the elements in $E \backslash F$, the set of female presidents who were not red-headed?
As for the second, let $E$ be the set of all even numbers, and $F$ be the set of all odd numbers. Then, what set is $E \backslash F$, the set of all even numbers that are not odd numbers?
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