1. The problem asks to list all subsets of the set $\{1, 2\}$.\n\n2. A subset is any combination of elements from the original set, including the empty set and the set itself.\n\n3. For a set with $n$ elements, the total number of subsets is $2^n$. Here, $n=2$, so there are $2^2=4$ subsets.\n\n4. List all subsets:\n- The empty set: $\emptyset$\n- The set containing only 1: $\{1\}$\n- The set containing only 2: $\{2\}$\n- The set containing both 1 and 2: $\{1, 2\}$\n\nFinal answer: The subsets of $\{1, 2\}$ are $\emptyset$, $\{1\}$, $\{2\}$, and $\{1, 2\}$.