Definition:Set Difference/Example

Definition

Let $S$ and $T$ be sets such that:

$S = \left\{{1, 2, 3}\right\}$
$T = \left\{{2, 3, 4}\right\}$

Let $\setminus$ denote set difference.

Then:

$S \setminus T = \left\{{1}\right\}$

while:

$T \setminus S = \left\{{4}\right\}$

It can immediately be seen that $S \setminus T$ is not commutative.