Chapter 3.4, Problem 12MS

Another two. Suppose S is the set defined by $S=\left\{1,2\right\}.$

Consider the following pairing of elements of S with elements of P(S):

Elements of S          Elements of P(S)

1           $\left\{2\right\}$

2           $\left\{1,\right\}$

Using the idea of Cantor’s proof, describe a particular subset of S that is not on this list.