## Thinking Mathematically (6th Edition)

$\left\{1, 5\right\}$
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 subsets of $\left\{1, 5\right\}$ are: $\left\{\right\} \\\left\{1\right\} \\\left\{5\right\} \\\left\{1, 5\right\}$ Notice that the first three subsets in the list are proper subsets. The only subset that is not a proper subset of the given set is: $\left\{1, 5\right\}$