# Category:Subsets

This category contains results about Subsets.
Definitions specific to this category can be found in Definitions/Subsets.

Let $S$ and $T$ be sets.

$S$ is a subset of a set $T$ if and only if all of the elements of $S$ are also elements of $T$.

This is denoted:

$S \subseteq T$

That is:

$S \subseteq T \iff \forall x: \paren {x \in S \implies x \in T}$

If the elements of $S$ are not all also elements of $T$, then $S$ is not a subset of $T$:

$S \nsubseteq T$ means $\neg \paren {S \subseteq T}$