2 This correspondence is incredibly useful for coding. Let's say that T = {1,2,3} - Example 11 proves that it takes 3 bits to represent all of the elements of P(T). (a) It takes 8 bits to represent the elements of P(P(T)). Following Table 3-3, what element is represented by (1,1,0,1,0,0,0,1)? (The element will be a set, and that set will contain sets.) (b) The power set exhibits what's known in mathematics as "superexponential growth. Find T), IP(T)], and |P(P(T)). According to Wolfram Alpha, how many decimal digits does the number P(P(P(T))) have? (This is a very, very large number - like, on the scale of number of atoms in the visible universe large.)