Answer
false
$\emptyset \subseteq \{\emptyset, \{\emptyset\}\}$
Work Step by Step
$\emptyset \not\subseteq \{\emptyset, \{\emptyset\}\}$
This is incorrect, for it should say:
$\emptyset \subseteq \{\emptyset, \{\emptyset\}\}$
By definition, an empty set is a subset of every set.