Subset

From CS2800 wiki


Definition: Subset
If [math]A [/math] and [math]B [/math] are sets, then [math]A [/math] is a subset of [math]B [/math] (written [math]A \href{/cs2800/wiki/index.php/%5Csubseteq}{\subseteq} B [/math]) if every [math]x \href{/cs2800/wiki/index.php/%5Cin}{\in} A [/math] is also in [math]B [/math]

For example, in the following Venn diagram, [math]A [/math] is a subset of [math]B [/math]:

Venn-subset.svg

Note the difference between [math]\href{/cs2800/wiki/index.php/%5Csubseteq}{\subseteq} [/math] and [math]\href{/cs2800/wiki/index.php/%5Cin}{\in} [/math]: [math]A \href{/cs2800/wiki/index.php/%5Csubseteq}{\subseteq} B [/math] says that [math]A [/math] is a set and that everything in [math]A [/math] is also in [math]B [/math]; [math]A \href{/cs2800/wiki/index.php/%5Cin}{\in} B [/math] means that [math]A [/math] 'itself' is an element of [math]B [/math].