EE 518 Homework 3 Due on Monday 2 00pm September 19 2016 Problem 1 For any set A B and C prove that 1 A B C A B A C 2 A B if and only if A B Problem 2 Let U be an ordered set and E U E 6 Suppose is a lower bound of E and is an upper bound of E Prove that Problem 3 Prove B n Ai i 1 n B Ai i 1 with A1 A2 An and B are any sets Problem 4 Consider the functions f x 1 1 x3 where x 6 1 and g x 1 sin x i Find the domain and range of a f g b f g c f g d g f x ii Find f 1 x g 1 x and specify domain and range iii Find f g x and specify its domain and range iv Are f g one to one mappings of If yes show it Problem 5 Show that lim n n 1 n 1 with the definition of limit of sequence Page 1 of 2 EE 518 Homework 3 Due on Monday 2 00pm September 19 2016 Problem 6 This is a Matlab exercise Write a function myfunc that will do the following 1 Accept a name of an Excel file as an input 2 Load the Excel file which should have a matrix with numbers between 0 and 100 Create your Excel file separately for you to test either using Matlab or manually Your function should recognize matrices of any size 3 Check how many elements of the matrix are less or equal to 50 and give as an output the number of elements as well as their sum Each dimension of your input matrix should be at least 5 If it is not your function should display the message Your input matrix is too small and give 0 for both outputs Remember to add a description Page 2 of 2