(20 points) Show that no compression scheme can be expected to compress all of the n-character files. Here a character is any of the 256, 8-bit characters. Here a compression scheme is an injective map C : S2n {0, 1)', where is the set of 256 characters, and {0, 1)' denotes the set of all finite strings of 0's and 1's. In other words, you need to show that for every such C, there exists some x 62n such that IC(x)1-8m as 8n is the initial size of the file. (20 points) Show that no compression scheme can be expected to compress all of the n-character files. Here a character is any of the 256, 8-bit characters. Here a compression scheme is an injective map C : S2n {0, 1)', where is the set of 256 characters, and {0, 1)' denotes the set of all finite strings of 0's and 1's. In other words, you need to show that for every such C, there exists some x 62n such that IC(x)1-8m as 8n is the initial size of the file