4. (powerset) (a) Express the powerset of {red, green, blue} in roster notation. (b) Consider the set S = {a,b,c,d). Suppose a subset of S is recorded as a 4-bit number with 1 iff the element is present. For example, the subset {b,c} would be recorded as 0110. Use this method to express the powerset of S as a set of 4-bit numbers. What do you observe? (c) Express the powerset of a set recursively, using set notation. That is, give the recurrence relation that expresses the powerset 2{41.4n+1} in terms of the powerset 2{41...), using set notation. Here are some examples of recurrence relations: the recurrence relation for Fibonacci numbers is F(n + 2) = F(n) + F(n +1); the recurrence relation for factorial is f(n +1) = f(n)*(n+1); the recurrence relation for 2" is 2n+1 = 2 * 2