The definition of partial order is:
Let $R$ be a relation on a set $S$. $R$ is a partial order if and only if the following three statements are true for every $a$, $b$, and $c$ in $S$:
Reflexive Property: $aRa$
Transitive Property: If $aRb$ and $bRc$, then $aRc$.
Antisymmetric Property: If $aRb$ and $bRa$, then $a=b$
I think $\{\{1\},\{2\},\{3\}\}$ is a partial order because, the reflexive property is satisfied, since $a⊆a$ for any set $a$ in $\{\{1\},\{2\},\{3\}\}$, the transitive and antisymmetric properties are satisfied because the antecedent of the implication is false. Is this correct?
Yes, the set $\{\{1\}, \{2\}, \{3\}\}$ is partially ordered by $\subseteq$ and your answer is essentially correct.
By the way, note that is not exact that the antecedent in the transitivity and symmetric conditions is always false, because $\{1\} \subseteq \{1\}$ and $\{2\} \subseteq \{2\}$ and $\{3\} \subseteq \{3\}$. But yes, you can say that transitivity and symmetry are satisfied in a trivial way.