Category:Definitions/Subsets

This category contains definitions related to Subsets.
Related results can be found in Category: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 $\neg \paren {S \subseteq T}$

Pages in category "Definitions/Subsets"

The following 11 pages are in this category, out of 11 total.