Empty Set is Subset of Power Set

Theorem

The empty set is a subset of all power sets:

$\forall S: \O \subseteq \powerset S$

Proof

Follows directly from Empty Set is Subset of All Sets.

$\blacksquare$

Also see

• Empty Set is Element of Power Set

Sources

• 1975: Bert Mendelson: Introduction to Topology (3rd ed.) ... (previous) ... (next): Chapter $1$: Theory of Sets: $\S 2$: Sets and Subsets: Exercise $1 \ \text{(e)}$