Assignment 3

Suggested Problems (not to be turned in)

• Rosen, Section 2.1, ex: 5, 13, 28, 32, 44
• Rosen, Section 2.2, ex: 15, 16, 29, 31
• Rosen, Section 2.3, ex: 2, 3, 7, 20, 21, 33
• Rosen, Section 2.5, ex: 1, 3, 10, 11
• Rosen, Section 3.1, ex: 7, 8, 13

Required Problems, due September 9

Submission Instructions

• Submissions are to be submitted on paper, with one submission from each assigned pair of students, unless a student has explicit (written) permission from the instructor.

• Both partners should collaborate on every problem, and both names should be at the top of the first page. Since this is a collaborative effort, both partners should agree that the work represents their agreement in the correctness of the answers, and the same grade will be recorded for each assignment.

• Problems for each section (each bullet item in the assignment) should begin on a new page, and problems within a section should be in numeric order.

• If a problem requires the writing of a Python program, then the submission should include a printout of the code, a listing of appropriate test runs, and a statement regarding how the test runs provide sufficient evidence to conclude the program works properly.

• Each problem from Rosen's text should be identified with its section number and problem number. Each problem written out as a separate bullet point should be identified in a phrase or sentence, so it is clear which question is being answered.

• When a problem asks for a conclusion, the solution must include both a statement of the conclusion and an argument justifying that conclusion.

• Answers should be placed in Section and problem order, so the first page (more if needed) should give answers for the problems in the first assignment bullet. Answers for subsequent bullets should be in the order of the bullets on the Assignment sheet.

• Although the rules of this course allow the use of sources beyond the discussions of a student pair, any outside references (e.g., from the textbook, from Web sources, from discussions with others, etc.) must be fully cited.

Problems to be Turned In

• Rosen, Section 2.1, ex: 6, 46
• Rosen, Section 2.2, ex: 18, 36
• Rosen, Section 2.2, ex: 20abc
• Rosen, Section 2.5, ex: 4
  • give a proof using a membership table
  • give a proof by explaining why an element in one side must also be in the other
• Rosen, Section 2.3, ex: 34, 42
• Finding a Maximum: Write a Python function findMax that taks an array of numbers as parameter and returns the maximum value.
  • Embed the function within a program, so the function can be tested.
  • Analyze the function: If the array has n elements, how many steps are required in the processing of findMax? Explain.
• As we have seen in class, the binary search is extremely fast relative to a linear search. Thus, one approach to finding a value within an array is to sort the array first and then use a binary search to locate the item (if it is present).
  • Is this algorithm efficient for any arrays, for some arrays, or fo arrays? Briefly explain your answer.
• Challenge Problem—Counter Sets and Onto Functions: Suppose f is a function from set A to set B, and suppose f is onto.
  • if set A is countable, must set B also be countable? (Prove or explain why not—likely with a counter example.)
  • if set B is countable, must set As also be countable? (Prove or explain why not—likely with a counter example.)

created July 22, 2021 revised September 6, 2021
For more information, please contact Henry M. Walker at walker@cs.grinnell.edu.