# Set Difference with Self is Empty Set

## Theorem

The set difference of a set with itself is the empty set:

$S \setminus S = \O$

## Proof

$S \subseteq S$

From Set Difference with Superset is Empty Set‎ we have:

$S \subseteq T \iff S \setminus T = \O$

Hence the result.

$\blacksquare$