## Thinking Mathematically (6th Edition)

$\subseteq$
RECALL: (1) A is a subset of B ($A \subseteq B$) if all elements of A are also elements of B. (2) A is a proper subset of B ($A \subset B$) if all elements of A are also in B but B has at least one element that is not in A. The set on the right is equal to $\left\{1, 2\right\}$ since the elements 1 and 2 are only repeated, and you only right unique elements inside a set. Thus, the set on the left is equal to the set on the right. All elements of the set on the left are also elements of the on the right. The set on the right has no element that is not an element of the other set. Therefore, the set on the left is a subset of the set on the right.