The two parts of this exercise show that for every set S (not necessarily countable), 2S is larger than S. a. For every S, describe a simple bijection from S to a subset of 2S. b. Show that for every...

The two parts of this exercise show that for every set S (not necessarily countable), 2S is larger than S. a. For every S, describe a simple bijection from S to a subset of 2S.

b. Show that for every S, there is no bijection from S to 2S . (You can copy the proof in Example 8.31, as long as you avoid trying to list the elements of S or making any reference to the countability of S.)