Instructions:This question has two steps. Please complete bo…

Instructions:This question has two steps. Please complete both steps.Step 1: Practice accessing the textbook by clicking the URL provided in the Instructions section of the Honorlock window.If you experience any difficulty, use the chat bubble in the bottom-right corner of the Honorlock window to contact an Honorlock specialist for assistance.Step 2: Answer the following question:Were you able to open the e-text?

You need to download the Exam template and use that to take…

You need to download the Exam template and use that to take this midterm.  You also need to submit all the 8 pages in the template, even if you do not write on all of them. 1.  In a village with 700 people, should there be at least two people with the same initials, where the initials of a person’s name are formed by the first letter of the first name followed by the first letter of the last name? Give reasons for your answer. (20 points) 2. Prove that a function f: S –>T is 1-1, if and only if for each subset A of S, f^{-1}(f(A) )=A. (30 points) 3. For the function f(x) = (x+1)/x,     (a) determine the domain and the range, with the domain as large as possible. (10 points)     (b) Is f 1-1? Justify your answer. (10 points)     (b) If the answer to (b) is yes, find a formula for the inverse of f. (10 points) 4.  Given subsets A, B and C of a big set U, suppose A  C  is a subset of B C and AC is a subset of B C. Then prove that A is a subset of B.  (20 points)