NO35 and NO36

The reversal of a string is the string consisting of the symbols of the string in reverse order. The reversal of the string w is denoted by wA 34. Find the reversal of the following bit strings. then am/# 2(m + n) + 1 for all (m, n 47. A partition of a positive integer n is a a 0101b) 11011 1000 1001 0111 as a sum of positive integers where the or the sum does not matter. For instance, 7 is a partition of 7. Let Pm equal the num partitions of m, and let Pm, be the numb ways to express m as the sum of positi exceeding n. a) Show that Pm P b) Show that the following recursive def 35. Give a recursive definition of the reversal of a string. Hint: First define the reversal of the empty string. Then write a string w of length n + Ias y, where is a string of length n, and express the reversal of w in terms of x and y.] 36. Use structural induction to prove that (wiw2RWw 37. Give a recursive definition of wi where w is a string and is correct: i is a nonnegative integer. (Here w represents the con- 38. Give a recursive definition of the set of bit strings that are 39. When does a string belong to the set A of bit strings de catenation of i copics of the string w) palindromes. fined recursively by if It Pm.m ) Find the number of partitions of 5 and recursive delinition Consider am inductive definition of a version o 40. Recursively define the set ol bit strines thal haye morefunction. This function was named after Wilhel where A is the empty string