Consider a set S of strings defined recursively as follows: ⚫ Base case: AES (A is the empty string, i.e. "" in programming.) Recursive rules: if x = S and yes then, 1. axbЄ S 2. xy Є S (a) List at least 8 distinct strings that are in S. You must use each recursive rule at least twice. (b) List at least 2 strings made up of only as and bs that are not in S.
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- S is a set of strings recursively defined as follows. Base case: Every variable from the set {a, b, c, d, e, f} is in S. Recursive rules: If x = S and y = S, then: 1. (x + y) Є S 2. x.yЄ S Indicate which expressions are in S. ☐ (d.e.a) a+b a.b.c ☐ (a + d).eCodeW For fun X C Solved https://codeworkou... 臺亂 CodeWorkout X272: Recursion Programming Exercise: Is Reverse For function isReverse, write the two missing base case conditions. Given two strings, this function returns true if the two strings are identical, but are in reverse order. Otherwise it returns false. For example, if the inputs are "tac" and "cat", then the function should return true. Examples: isReverse("tac", "cat") -> true Your Answer: 1 public boolean isReverse(String s1, String s2) { 2. if > 3. 4. else if > return true; return false; 5. 6. else { String s1first = String s2last return s1first.equals (s2last) && 51. substring(0, 1); s2, substring(s2.length() 1); 7. 8. 6. isReverse(s1.substring(1), s2.substring(0, s2.length() 1)); { 12} 1:11AM 50°F Clear 12/4/2021The following recursive definition of a set S over {a, b, c, d}. Basis: "", a, b, c E S. Recursive Step: If ax E S, then bax ES and cax E S. If bx € S, then cbx € S. If cx = S, then bax ES and bcx = S. If dx E S, then ddx E S. Closure: SE S only if it is a, b or c or it can be obtained from a, b or c using finitely many operations of the Recursive Step. a) What recursive step can be removed from the above definition and why? b) Derive from the definition of S that bcbc S. c) Explain why baa & S.
- Exercise 1: The number of combinations CR represents the number of subsets of cardi- nal p of a set of cardinal n. It is defined by C = 1 if p = 0 or if p = n, and by C = C+ C in the general case. An interesting property to nxC calculate the combinations is: C : Write the recursive function to solve this problem.Computer Science A set M is defined recursively by: 2 and 3 belong to M If x and y belong to M then so does x·y Which of the following numbers belong to M if x≠y?PYTHON RECURSIVE FUNCTION Write a python program that lists all ways people can line up for a photo (all permutations of a list of strings). The program will read a list of one word names, then use a recursive method to create and output all possible orderings of those names, one ordering per line. When the input is: Julia Lucas Mia then the output is (must match the below ordering): Julia Lucas Mia Julia Mia Lucas Lucas Julia Mia Lucas Mia Julia Mia Julia Lucas Mia Lucas Julia
- Write a recursive function to print all the permutations of a string. For example, for the string abc, the printout is:abcacbbacbcacabcba(Hint: Define the following two functions. The second function is a helper function.def displayPermuation(s):def displayPermuationHelper(s1, s2): The first function simply invokes displayPermuation(" ", s). The secondfunction uses a loop to move a character from s2 to s1 and recursively invokes t with a new s1 and s2. The base case is that s2 is empty and prints s1 to the console.)Write a test program that prompts the user to enter a string and displays all its permutations.Computer Science The language L = { | L(M) contains at least 4 strings that begin and end with 1 } IS an R.E. Non-Recursive language (trust me it IS ). What about the compliment of L? Is it RECURSIVE, R.E. Non-Recursive, or NON-R.E.?2. Sum: a recursive function that computes the sum of integers 1, 2, 3, …., n for a given number n. So Sum(6) should return 1 + 2 + 3 + 4 + 5 + 6 , i.e. 21.sum(n) = n + sum(n-1)
- 31Pascal's triangle is a useful recursive definition that tells us the coefficients in the expansion of the polynomial (x + a)^n. Each element in the triangle has a coordinate, given by the row it is on and its position in the row (which you could call a column). Every number in Pascals triangle is defined as the sum of the item above it and the item above it and to the left. If there is a position that does not have an entry, we treat it as if we had a 0 there. *picture of the pascals triangle* Given the following recursive function signature, write the recursive function that takes a row and a column and finds the value at that position in the triangle. Assume that the triangle starts at row 0 and column 0. Examples: pascal(2, 1) -> 2, pascal(1, 2) -> 0 public int pascal(int row, int column) { }PHP A factorial of any given integer, n , is the product of all positive integers between 1 and n inclusive. So the factorial of 4 is 1 × 2 × 3 × 4 = 24, and the factorial of 5 is 1 × 2 × 3 × 4 × 5 = 120. This can be expressed recursively as follows: ❑ If n == 0, return 1. (This is the base case) ❑ If n > 0, multiply numbers from n down to 1. Write a PHP function to display the factorials of the integers up to the given value(argument). Any format could be used for displaying. Write the recursive version of the same function to display the factorials of the integers up to the given value(argument). Any format could be used for displaying.