1.14.1: Big-O True or False 1) A Θ (n) algorithm is O (n) {Ans: True This is as true as our original program was theta (n). You can achieve big O (n) without altering your program at all.}4.4.2: The bijection mapping power sets to strings 1) What is f({1,4})? 2) Which element is not in f^-1 (1101)? 3) How many elements are in the set f^-1(0000)? {Ans: }3.7.3: Computing sums of geometric and arithmetic sequences Give numerical values for the following summations. 2) k = 0 to 9 ∑ 2^k {Ans: }3.21.2: Matching characteristic equations to linear recurrence relations Do the problem directly on the course material {Ans: See course material}Exercise 3.21.3: Solving linear homogeneous recurrence relations Solve each of the following recurrence equations with the given initial values. (a) b_n = b_(n − 1) + 12b_(n − 2). Initial values: b_0 = −2, b_1 = 20 (b) b_n = 3b_(n − 1) + 4b_(n − 2). Initial values: b_0 = 4, b_1 = 1 {Ans: }2.9.1: Brute force factoring. 1) Suppose that the slightly better brute force algorithm for factoring is given the number 653117 as input. How many numbers would the algorithm have