1. [10 marks] we begin with some mathematics regarding uncountability. let n = {0, 1, 2, 3, . .} denote the set of natural numbers. (a) [5 marks] prove that the set of binary numbers has the same size as n by giving a bijection between the binary numbers and n. (b) [5 marks] let b denote the set of all infinite sequences over the english alphabet. show that b is uncountable using a proof by diagonalization.

Think about some of the most memorable and forgettable games ever created. they can be games that were discussed in this unit or otherwise. what are some of the consistent factors that made certain games memorable to you? what were some of the consistent factors that made certain games forgettable to you? why? explain.

What type of computer network ensures high security ?

Consider the following function main: int main() { int alpha[20]; int beta[20]; int matrix[10][4]; . . } a. write the definition of the function inputarray that prompts the user to input 20 numbers and stores the numbers into alpha. b. write the definition of the function doublearray that initializes the elements of beta to two times the corresponding elements in alpha. make sure that you prevent the function from modifying the elements of alpha. c. write the definition of the function copyalphabeta that stores alpha into the first five rows of matrix and beta into the last five rows of matrix. make sure that you prevent the function from modifying the elements of alpha and beta. d. write the definition of the function printarray that prints any onedimensional array of type int. print 15 elements per line. e. write a c11 program that tests the function main and the functions discussed in parts a through d. (add additional functions, such as printing a two-dimensional array, as needed.)