EE 518 : Homework #3 Due on Monday 2:00pm, September 19, 2016Problem 1For any set A, B and C, prove that1. A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)2. A ⊂ B if and only if A − B = ∅Problem 2Let U be an ordered set and E ⊂ U, E 6= ∅. Suppose α is a lower bound of E and βis an upper bound of E. Prove that α ≤ β.Problem 3ProveB \n\i=1Ai=n[i=1(B \ Ai)with A1, A2, . . . , Anand B are any sets.Problem 4Consider the functions f(x) =11−x3where 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 5Show thatlimn→∞nn + 1= 1with the definition of limit of sequence.Page 1 of 2EE 518 : Homework #3 Due on Monday 2:00pm, September 19, 2016Problem 6This is a Matlab exercise. Write a function myfunc that will do the following:1. Accept a name of an Excel file as an input2. Load the Excel file, which should have a matrix with numbers between 0 and 100. Create your Excelfile separately for you to test either using Matlab or manually. Your function should recognize matricesof any size.3. Check how many elements of the matrix are less or equal to 50 and give as an output the number ofelements, as well as their sum.Each dimension of your input matrix should be at least 5. If it is not, your function should display themessage ”Your input matrix is too small” and give 0 for both outputs. Remember to add a description.Page 2 of