For each of the following problems (described informally in English), first define a language L{0,1} that formalizes the problem. Then describe the correspondence between: (i) instances of the problem with their answers, and (2) strings and their (non-)membership in the language. As an example, consider the problem: "Given a PNG image, which half (top or bottom) most resembles a cat?" A correct answer would be: L={I:I is a PNG image whose top half resembles a cat more than its bottom half }. An image I corresponds to the string encoding I. If I 's top half resembles a cat more than its bottom half, then IL; otherwise, I/L. (a) Given two integers, which one is larger? (You may break ties however you like.) (b) Given a binary string s, does s1s (i.e., s concatenated to 1 concatenated to s ) have more 0s, or more 1s? (c) We call a base-2 representation of a positive integer standard if the representation has no leading 0s (i.e., it starts with 1). Given a positive integer n, for its standard base-2 representation, which of the following quantities is greater: the sum of the digits, or the product of the digits? (You may break ties arbitrarily.)