One set, A, is a subset of another, B, if and only if all elements of A are elements of B.

A set is any collection of elements. Sets can be related to each other in various ways; one important way sets can be related is that one set could be a subset of another. One set, $A$, is a subset of another, $B$, if and only if all elements of $A$ are elements of $B$. This is denoted $A \subseteq B$. Notably, $A$ can be a subset of $B$ even if there are no elements in $B$ that are not also in $A$ (i.e., they contain exactly the same elements). When $B$ contains additional elements that are not in $A$, $A$ is called a "proper subset" of $B$. This is denoted $A \subset B$. The same relationship between these sets can be indicated by calling $B$ a "superset", or "proper superset", of $A$ ($B \supseteq A$, or $B \supset A$, respectively), but referring to the [potentially] smaller set as a subset is more common.