For $X$ any topological space, show that the following presheaves of sets over $X$ are in facts sheaves:
Fixing an open $V \subseteq X$, let
$$ h_V(U)= \quad \begin{cases} \text{singleton} & U \subseteq V\\ \emptyset & U \nsubseteq V \\ \end{cases} $$
Solution: Both the monopresheaf and the gluing condition are meaningless for $U \nsubseteq V$, so they trivially hold. For $U \subseteq V$ both conditions are valid as there is only one possible section. Therefore all restrictions and gluings are well-defined.
My question is: could please any one explain to me how I can justify my answer in more detail?