1 Question 1: 40 Points (a) Consider that NSU IEEE chapter has 40 members and we are interested to elect a president, treasurer, general secretary, organizing secretary, vice president and observer for NSU IEEE. How many ways do we have to choose candidates for those vaccant posts? Also, how many alternative ways do we have to select an executive committee consists of 15 members from a pool of 40 members. Justify your answer. (b) Suppose we have three alterntaive types of graph represented using the standard notation Kn, Cn and Wn. Calculated the number of nodes and edges in all the three graph types. Also, draw each of the three graphs for n = 5. (c) Prove that in any undirected graph if we calculate the degrees of all nodes we will find an even number of nodes of odd degrees. 3 Question 3: 30 Points (a) Give a recursive definition of a set A defined as: A = {(1,7)|x Z+, y Zt, and x = 2n + 1, y = 2m + 1, where m, n represent any natural numbers). List the elements of S produced by first 3 iterations of the recursive definition you provide. (b) Assume that Z is the domain of a hypothetical function f and is defined as : Z+Z+. Provide an explicit algebraic expression of f such that f is neither injective nor surjective